共查询到20条相似文献,搜索用时 15 毫秒
1.
Wu Liangsen 《数学学报(英文版)》1992,8(4):406-412
LetA, B be unitalC
*-algebras,D
A
1
the set of all completely positive maps ϕ fromA toM
n
(C), with Tr ϕ(I)≤1(n≥3). If Ψ is an α-invariant affine homeomorphism betweenD
A
1
andD
B
1
with Ψ (0)=0, thenA is*-isomorphic toB.
Obtained results can be viewed as non-commutative Kadison-Shultz theorems.
This work is supported by the National Natural Science Foundation of China. 相似文献
2.
M. F. Gamal' 《Journal of Mathematical Sciences》1998,92(1):3589-3596
Let B be a Blaschke product with simple zeros in the unit disk, let Λ be the set of its zeros, and let ϕ∈H∞. It is known that ϕ+BH∞ is a weak* generator of the algebra H∞/BH∞ if (for B that satisfy the Carleson condition (C)) and only if the sequence ϕ(Λ) is a weak* generator of the algebra l∞. In this paper, we show that for any Blaschke product B with simple zeros that does not satisfy condition (C), there exists
B=B1·…·BN, where N ∈ℕ, and B1, …, BN are Blaschke products satisfying condition (C), there exists a function ϕ∈H∞ such that ϕ(Λ) is a weak* generator of the algebra l∞, and ϕ+BH∞ is not a weak* generator of the algebra H∞/BH∞. Bibliography: 12 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 73–85.
Translated by M. F. Gamal'. 相似文献
3.
Let H be a complex Hilbert space of dimension greater than 2, and B(H) denote the Banach algebra of all bounded linear operators on H. For A, B ∈ B(H), define the binary relation A ≤* B by A*A = A*B and AA* = AB*. Then (B(H), “≤*”) is a partially ordered set and the relation “≤*” is called the star order on B(H). Denote by Bs(H) the set of all self-adjoint operators in B(H). In this paper, we first characterize nonlinear continuous bijective maps on B
s
(H) which preserve the star order in both directions. We characterize also additive maps (or linear maps) on B(H) (or nest algebras) which are multiplicative at some invertible operator. 相似文献
4.
S. J. Bhatt 《Proceedings Mathematical Sciences》2001,111(1):65-94
UniversalC*-algebrasC*(A) exist for certain topological *-algebras called algebras with aC*-enveloping algebra. A Frechet *-algebraA has aC*-enveloping algebra if and only if every operator representation ofA mapsA into bounded operators. This is proved by showing that every unbounded operator representation π, continuous in the uniform
topology, of a topological *-algebraA, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through
the enveloping pro-C*-algebraE(A) ofA. Given aC*-dynamical system (G,A,α), any topological *-algebraB containingC
c
(G,A) as a dense *-subalgebra and contained in the crossed productC*-algebraC*(G,A,α) satisfiesE(B) =C*(G,A,α). IfG = ℝ, ifB is an α-invariant dense Frechet *-subalgebra ofA such thatE(B) =A, and if the action α onB ism-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS(ℝ,B,α) satisfiesE(S(ℝ,B,α)) =C*(ℝ,A,α). WhenG is a Lie group, theC
∞-elementsC
∞(A), the analytic elementsC
ω(A) as well as the entire analytic elementsC
є(A) carry natural topologies making them algebras with aC*-enveloping algebra. Given a non-unitalC*-algebraA, an inductive system of idealsI
α is constructed satisfyingA =C*-ind limI
α; and the locally convex inductive limit ind limI
α is anm-convex algebra with theC*-enveloping algebraA and containing the Pedersen idealK
a
ofA. Given generatorsG with weakly Banach admissible relationsR, we construct universal topological *-algebraA(G, R) and show that it has aC*-enveloping algebra if and only if (G, R) isC*-admissible. 相似文献
5.
L. Yu. Glebskii 《Mathematical Notes》1999,65(1):31-40
Theorems are proved establishing a relationship between the spectra of the linear operators of the formA+Ωg
iBigi
−1 andA+B
i, whereg
i∈G, andG is a group acting by linear isometric operators. It is assumed that the closed operatorsA andB
i possess the following property: ‖B
iA−1gBjA−1‖→0 asd(e,g)→∞. Hered is a left-invariant metric onG ande is the unit ofG. Moreover, the operatorA is invariant with respect to the action of the groupG. These theorems are applied to the proof of the existence of multicontour solutions of dynamical systems on lattices.
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 37–47, January, 1999. 相似文献
6.
Kunyu Guo 《Arkiv f?r Matematik》2000,38(1):97-110
For an essentially normal operatorT, it is shown that there exists a unilateral shift of multiplicitym inC
*
(T) if and only if γ(T)≠0 and γ(T)/m. As application, we prove that the essential commutant of a unilateral shift and that of a bilateral shift are not isomorphic
asC
*
-algebras. Finally, we construct a naturalC
*
-algebra ε + ε* on the Bergman spaceL
a
2
(B
n
), and show that its essential commutant is generated by Toeplitz operators with symmetric continuous symbols and all compact
operators.
Supported by NSFC and Laboratory of Mathematics for Nonlinear Science at Fudan University. 相似文献
7.
The paper aims at developing a theory of nuclear (in the topological algebraic sense) pro-C*-algebras (which are inverse limits of C*-algebras) by investigating completely positive maps and tensor products. By using the structure of matrix algebras over a
pro-C*-algebra, it is shown that a unital continuous linear map between pro-C*-algebrasA andB is completely positive iff by restriction, it defines a completely positive map between the C*-algebrasb(A) andb(B) consisting of all bounded elements ofA andB. In the metrizable case,A andB are homeomorphically isomorphic iff they are matricially order isomorphic. The injective pro-C*-topology α and the projective pro-C*-topology v on A⊗B are shown to be minimal and maximal pro-C*-topologies; and α coincides with the topology of biequicontinous convergence iff eitherA orB is abelian. A nuclear pro-C*-algebraA is one that satisfies, for any pro-C*-algebra (or a C*-algebra)B, any of the equivalent requirements; (i) α =v onA ⊗B (ii)A is inverse limit of nuclear C*-algebras (iii) there is only one admissible pro-C*-topologyon A⊗B (iv) the bounded partb(A) ofA is a nuclear C⊗-algebra (v) any continuous complete state map A→B* can be approximated in simple weak* convergence by certain finite rank complete state maps. This is used to investigate permanence properties of nuclear pro-C*-algebras pertaining to subalgebras, quotients and projective and inductive limits. A nuclearity criterion for multiplier
algebras (in particular, the multiplier algebra of Pedersen ideal of a C*-algebra) is developed and the connection of this C*-algebraic nuclearity with Grothendieck’s linear topological nuclearity is examined. A σ-C*-algebraA is a nuclear space iff it is an inverse limit of finite dimensional C*-algebras; and if abelian, thenA is isomorphic to the algebra (pointwise operations) of all scalar sequences. 相似文献
8.
We study the injectivity properties of the spherical mean value operators associated to the Gelfand pairs (H
n,K), whereK is a compact subgroup ofU(n). We show that these spherical mean value operators are injective onL
p Hn) for 1≤p<∞. Forp=∞, these operators are not injective. Nevertheless, if the spherical meansf*μ
i
overK-orbits of sufficiently many points (z
i,t
i) ∈H
n vanish, we identify a necessary and sufficient condition on the points (z
i,t
i) which guaranteesf=0. ForK=U(n), this is equivalent to the condition for the two-radius theorem.
Research supported by N.B.H.M. Research Grant, Govt. of India. 相似文献
9.
Let L(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L(H), we define the elementary operator Δ
A
: L(H) → L(H) by Δ
A
(X) = AXA − X. In this paper we study the class of operators A ∈ L(H) which have the following property: ATA = T implies AT*A = T* for all trace class operators T ∈ C
1(H). Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the
fact that the ultraweak closure of the range of Δ
A
is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints
operators. 相似文献
10.
T. Shulman 《Journal of Mathematical Sciences》2009,159(6):894-903
We consider maps defined on a real space Asa of all self-adjoint elements of a C*-algebra A commuting with the conjugation by unitaries: F(u* au) = u* F(a)u for any a ∈ A
sa, u ∈ (A). In the case where A is a full matrix algebra, there is a functional realization of these maps (in terms of multivariable functions) and analytical
properties of these maps can be expressed in terms of corresponding functions. In the present work, these results are generalized
to the class of uniformly hyperfinite C*-algebras and to the algebra of all compact operators in a Hilbert space.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 213–227, 2007. 相似文献
11.
We show that if A is a Hilbert–space operator, then the set of all projections onto hyperinvariant subspaces of A, which is contained in the von Neumann algebra υN(A) that is generated by A, is independent of the representation of υ N(A), thought of as an abstract W*–algebra. We modify a technique of Foias, Ko, Jung and Pearcy to get a method for finding nontrivial hyperinvariant subspaces
of certain operators in finite von Neumann algebras. We introduce the B–circular operators as a special case of Speicher's B–Gaussian operators in free probability theory, and we prove several results about a B–circular operator z, including formulas for the B–valued Cauchy– and R–transforms of z*z. We show that a large class of L∞([0,1])–circular operators in finite von Neumann algebras have nontrivial hyperinvariant subspaces, and that another large
class of them can be embedded in the free group factor L(F3). These results generalize some of what is known about the quasinilpotent DT–operator.
Supported in part by NSF Grant DMS-0300336.
with an Appendix by Gabriel Tucci 相似文献
12.
Lars Kadison 《Applied Categorical Structures》2006,14(5-6):605-625
A depth two extension A | B is shown to be weak depth two over its double centralizer V
A
(V
A
(B)) if this is separable over B. We consider various examples and non-examples of depth one and two properties. Depth two and its relationship to direct
and tensor product of algebras as well as cup product of relative Hochschild cochains is examined. Section 6 introduces a
notion of codepth two coalgebra homomorphism g : C → D, dual to a depth two algebra homomorphism. It is shown that the endomorphism ring of bicomodule endomorphisms End
D
C
D
forms a right bialgebroid over the centralizer subalgebra g
* : D
* → C
* of the dual algebra C
*.
Dedicated to Daniel Kastler on his eightieth birthday. 相似文献
13.
Miroslav Engli 《Arkiv f?r Matematik》1992,30(1):227-243
In this paper it is shown that Toeplitz operators on Bergman space form a dense subset of the space of all bounded linear
operators, in the strong operator topology, and that their norm closure contains all compact operators. Further, theC
*-algebra generated by them does not contain all bounded operators, since all Toeplitz operators belong to the essential commutant
of certain shift. The result holds in Bergman spacesA
2(Ω) for a wide class of plane domains Ω⊂C, and in Fock spacesA
2(C
N),N≧1. 相似文献
14.
Laura B. Mastrangelo 《Israel Journal of Mathematics》1993,84(1-2):33-51
SupposeB is a type IC
*-algebra admitting a diagonalD in the sense of Kumjian, and letE be the conditional expectation fromB ontoD. A subalgebraA ofB is called triangular with diagnoalD ifA∩A*=D.
Theorem: Under the above assumptions the Jacobson radical ofA equals the intersection ofA with the kernel of the conditional expectationE.
Although the statement of the theorem is coordinate free, the proof requires the use of coordinates in essential ways.
A theorem by Kumjian allows us to represent everyC
*-algebra admitting a diagonal as theC
*-algebra of a certain groupoid. This enables us to apply the techniques of topological groupoids as developed by Renault and
Muhly. A very convenient way of expressing a triangular subalgebra of theC
*-algebra of a T-groupoid is given by the Spectral Theorem for Bimodules, due to Qui, which is a descendent of the Spectral
Theorem for Bimodules due to Muhly and Solel, and to Muhly, Saito and Solel in the context of von Neumann algebras. 相似文献
15.
Dieter Bothe 《Israel Journal of Mathematics》1998,108(1):109-138
Given anm-accretive operatorA in a Banach spaceX and an upper semicontinuous multivalued mapF: [0,a]×X→2
X
, we consider the initial value problemu′∈−Au+F(t,u) on [0,a],u(0)=x
0. We concentrate on the case when the semigroup generated by—A is only equicontinuous and obtain existence of integral solutions if, in particular,X* is uniformly convex andF satisfies β(F(t,B))≤k(t)β(B) for all boundedB⊂X wherek∈L
1([0,a]) and β denotes the Hausdorff-measure of noncompactness. Moreover, we show that the set of all solutions is a compactR
δ-set in this situation. In general, the extra condition onX* is essential as we show by an example in whichX is not uniformly smooth and the set of all solutions is not compact, but it can be omited ifA is single-valued and continuous or—A generates aC
o-semigroup of bounded linear operators. In the simpler case when—A generates a compact semigroup, we give a short proof of existence of solutions, again ifX* is uniformly (or strictly) convex. In this situation we also provide a counter-example in ℝ4 in which no integral solution exists.
The author gratefully acknowledges financial support by DAAD within the scope of the French-German project PROCOPE. 相似文献
16.
Let G be a compact group whose local weight b(G) has uncountable cofinality. Let H be an amenable locally compact group and A(G × H) be the Fourier algebra of G × H. We prove that the group von Neumann algebra VN(G × H) = A(G × H)* has the weak uniform A(G × H)** factorization property of level b(G). As a corollary we show that A(G × H) is strongly Arens irregular, and the topological centre of UC
2(G × H)* is equal to the Fourier–Stieltjes algebra B(G × H). 相似文献
17.
18.
A bijective linear mapping between two JB-algebrasA andB is an isometry if and only if it commutes with the Jordan triple products ofA andB. Other algebraic characterizations of isometries between JB-algebras are given. Derivations on a JB-algebraA are those bounded linear operators onA with zero numerical range. For JB-algebras of selfadjoint operators we have: IfH andK are left Hilbert spaces of dimension ≥3 over the same fieldF (the real, complex, or quaternion numbers), then every surjective real linear isometryf fromS(H) ontoS(K) is of the formf(x)=UoxoU
−1 forx inS(H), whereτ is a real-linear automorphism ofF andU is a real linear isometry fromH ontoK withU(λh)=τ(λ)U(h) for λ inF andh inH.
Supported by Acción Integrada Hispano-Alemana HA 94 066 B 相似文献
19.
Shi Niandong 《数学学报(英文版)》1988,4(1):14-17
A Boolean algebraB=
is recursive ifB is a recursive subset of ω and the operations Λ, v and ┌ are partial recursive. A subalgebraC ofB is recursive an (r.e.) ifC is a recursive (r.e.) subset of B. Given an r.e. subalgebraA, we sayA can be split into two r.e. subalgebrasA
1 andA
2 if (A
1 ∪A
2)*=A andA
1 ∩A
2={0, 1}. In this paper we show that any nonrecursive r.e. subalgebra ofB can be split into two nonrecursive r.e. subalgebras ofB. This is a natural analogue of the Friedberg's splitting theorem in ω recursion theory. 相似文献
20.
Yongge Tian 《Mediterranean Journal of Mathematics》2012,9(1):47-60
The decomposition of a Hermitian solution of the linear matrix equation AXA* = B into the sum of Hermitian solutions of other two linear matrix equations A1X1A*1 = B1{A_{1}X_{1}A^{*}_{1} = B_{1}} and A2X2A*2 = B2{A_{2}X_{2}A^*_{2} = B_{2}} are approached. As applications, the additive decomposition of Hermitian generalized inverse C
− = A
− + B
− for three Hermitian matrices A, B and C is also considered. 相似文献