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1.
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
2.
Let H be a Hilbert space and A be a standard *-subalgebra of B(H). We show that a bijective map Ф : A →A preserves the Lie-skew product AB - BA* if and only if there is a unitary or conjugate unitary operator U ∈A(H) such that Ф(A) = UAU* for all A ∈ A, that is, Фis a linear * -isomorphism or a conjugate linear *-isomorphism. 相似文献
3.
Xiao Xia ZHANG 《数学学报(英文版)》2006,22(4):1221-1226
In this paper, we first prove that the θ-deformation Uθ(2) of U(2) constructed by Connes and Violette is our special case of the quantum group Uq(2) constructed in our previous paper. Then we will show that the set of truces on the C^* -algebra Uθ, θ irrational, is determined by the set of the truces on a subalgebra of Uθ. 相似文献
4.
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
5.
6.
In this paper, a class of generalized Verma modules M(V) over some Block type Lie algebra ℬ(G) are constructed, which are induced from nontrivial simple modules V over a subalgebra of ℬ(G). The irreducibility of M(V) is determined.
相似文献
7.
For every algebraU there is an algebraU
* with (up to isomorphism) the same endomorphism, subalgebra and congruence structure as that ofU, for which every finitely generated subalgebra and every finitely generated congruence ofU
* is singly generated. The theorem is proved in a somewhat more general category theoretic context.Presented by R. W. Quackenbush.This author's research was supported by an OTKA grant from Hungary.This author's research was supported by NSERC, The Natural Sciences and Engineering Research Council of Canada. 相似文献
8.
A result previously known only for certain ordered Banach spaces is generalized to arbitrary real Banach spaces. Let ℒ be
the Banach algebra of operators generated by theL-projections of a real Banach spaceU, and let ℳ (U
* be the bounded operators on the dual spaceU
* with adjoint in ℒ(U
**. Then the adjoint operation maps ℒ (U) onto ℳ (U
*). In particular, anyM-projection ofU
* is weak* continuous.
Supported in part by the National Science Foundation. 相似文献
9.
N. W. Sauer 《Combinatorica》2006,26(2):231-253
Given a universal binary countable homogeneous structure U and n∈ω, there is a partition of the induced n-element substructures of U into finitely many classes so that for any partition C0,C1, . . .,Cm−1 of such a class Q into finitely many parts there is a number k∈m and a copy U* of U in U so that all of the induced n-element substructures of U* which are in Q are also in Ck.
The partition of the induced n-element substructures of U is explicitly given and a somewhat sharper result as the one stated above is proven.
* Supported by NSERC of Canada Grant # 691325. 相似文献
10.
11.
Haïkel Skhiri 《Acta Appl Math》2010,112(3):347-356
Let m(T) and q(T) be respectively the minimum and the surjectivity moduli of T∈ℬ(X), where ℬ(X) denotes the algebra of all bounded linear operators on a complex Banach space X. If there exists a semi-invertible but non-invertible operator in ℬ(X) then, given a surjective unital linear map φ: ℬ(X)⟶ℬ(X), we prove that m(T)=m(φ(T)) for all T∈ℬ(X), if and only if, q(T)=q(φ(T)) for all T∈ℬ(X), if and only if, there exists a bijective isometry U∈ℬ(X) such that φ(T)=UTU
−1 for all T∈ℬ(X). 相似文献
12.
Richard Holzer 《Algebra Universalis》2007,57(4):419-453
Greechie diagrams are well known graphical representations of orthomodular partial algebras, orthomodular posets and orthomodular
lattices. For each hypergraph D a partial algebra ⟦D⟧ = (A; ⊕, ′, 0) of type (2,1,0) can be defined. A Greechie diagram can be seen as a special hypergraph: different points of the
hypergraph have different interpretations in the corresponding partial algebra ⟦D⟧, and each line in the hypergraph has a maximal Boolean subalgebra as interpretation, in which the points are the atoms.
This paper gives some generalisations of the characterisations in [K83] and [D84] of diagrams which represent orthomodular
partial algebras (= OMAs), and we give an algorithm how to check whether a given hypergraph D is an OMA-diagram whose maximal Boolean subalgebras are induced by the lines of the hypergraph.
Received July 22, 2004; accepted in final form February 1, 2007. 相似文献
13.
Donald I. Cartwright 《Monatshefte für Mathematik》2001,247(1):93-109
To any locally finite thick building of type there is naturally associated a commutative algebra of operators. When is constructed from a local field F with local ring , and , then is isomorphic to the convolution algebra of compactly supported bi-K-invariant functions on PGL(n+1,F). We give a proof, valid for any , that the multiplicative functionals on may all be expressed in terms of Hall–Littlewood polynomials. Regarding as a subalgebra of the C *-algebra of bounded operators on the space of square summable functions on the vertex set of , we find the spectrum of the C *-algebra , the closure of . This generalizes results obtained in [3] when n = 1 and in [5] when n = 2. 相似文献
14.
Lars Schäfer 《Annals of Global Analysis and Geometry》2007,32(2):125-145
In this paper we study para-tt *-bundles (TM, D, S) on the tangent bundle of an almost para-complex manifold (M, τ). We characterise those para-tt *-bundles with ${\nabla=D + S}In this paper we study para-tt
*-bundles (TM, D, S) on the tangent bundle of an almost para-complex manifold (M, τ). We characterise those para-tt
*-bundles with induced by the one-parameter family of connections given by and prove a uniqueness result for solutions with a para-complex connection D. Flat nearly para-K?hler manifolds and special para-complex manifolds are shown to be such solutions. We analyse which of
these solutions admit metric or symplectic para-tt
*-bundles. Moreover, we give a generalisation of the notion of a para-pluriharmonic map to maps from almost para-complex manifolds
(M, τ) into pseudo-Riemannian manifolds and associate to the above metric and symplectic para-tt
*-bundles generalised para-pluriharmonic maps into , respectively, into SO
0(n,n)/U
π(C
n
), where U
π(C
n
) is the para-complex analogue of the unitary group.
相似文献
15.
16.
C. Ogle 《K-Theory》2005,36(3-4):345-369
We show that the Strong Novikov Conjecture for the maximal C*-algebra C*(π) of a discrete group π is equivalent to a statement in topological K-theory for which the corresponding statement in algebraic K-theory is always true. We also show that for any group π, rational injectivity of the full assembly map for K*t(C*(π)) follows from rational injectivity of the restricted assembly map.
(Received: February 2006) 相似文献
17.
Spaces of analytic functions of Hardy-Bloch type 总被引:1,自引:1,他引:0
For 0<p≤∞ and 0<q≤∞, the space of Hardy-Bloch type ℬ(p,q) consists of those functionsf which are analytic in the unit diskD such that (1−r)M
p
(r,f′)⊂L
q
(dr/(1−r)). We note that ℬ(∞,∞) coincides with the Bloch space ℬ and that ℬ⊂ℬ(p,∞) for allp. Also, the space ℬ(p,p) is the Dirichlet spaceD
p−1
p
.
We prove a number of results on decomposition of spaces with logarithmic weights which allow us to obtain sharp results about
the mean growth of the ℬ(p,q). In particular, we prove that iff is an analytic function inD and 2≤p<∞, then the conditionM
p
(r,f′)=O((1−r)−1), asr→1, implies that
. This result is an improvement of the well-known estimate of Clunie and MacGregor and Makarov about the integral means of
Bloch functions, and it also improves the main result in a recent paper by Girela and Peláez. We also consider the question
of characterizing the univalent functions in the spaces ℬ(p,2), 0<p<∞, and in some other related spaces and give some applications of our estimates to study the Carleson measures for the spaces
ℬ(p,2) andD
p−1
p
.
The first and third authors were supported by grants from “E1 Ministerio de Educación y Ciencia”, Spain (MTN2004-00078 and
MTN2004-21420-E) and by a grant from “La Junta de Andalucía” (FQM-210).
The second author was supported in part by MNZŽS Grant, No. ON144010, Serbia. 相似文献
18.
Frank Harary 《Numerische Mathematik》1962,4(1):128-135
LetM be a square matrix whose entries are in some field. Our object is to find a permutation matrixP such thatPM P
–1 is completely reduced, i.e., is partitioned in block triangular form, so that all submatrices below its diagonal are 0 and all diagonal submatrices are square and irreducible. LetA be the binary (0, 1) matrix obtained fromM by preserving the 0's ofM and replacing the nonzero entries ofM by 1's. ThenA may be regarded as the adjacency matrix of a directed graphD. CallD strongly connected orstrong if any two points ofD are mutually reachable by directed paths. Astrong component ofD is a maximal strong subgraph. Thecondensation D
* ofD is that digraph whose points are the strong components ofD and whose lines are induced by those ofD. By known methods, we constructD
* from the digraph,D whose adjacency matrixA was obtained from the original matrixM. LetA
* be the adjacency matrix ofD
*. It is easy to show that there exists a permutation matrixQ such thatQA
*
Q
–1 is an upper triangular matrix. The determination of an appropriate permutation matrixP from this matrixQ is straightforward.This was an informal talk at the International Symposium on Matrix Computation sponsored by SIAM and held in Gatlinburg, Tennessee, April 24–28, 1961 and was an invited address at the SIAM meeting in Stillwater, Oklahoma on August 31, 1961 相似文献
19.
Donald I. Cartwright 《Monatshefte für Mathematik》2001,133(2):93-109
To any locally finite thick building of type there is naturally associated a commutative algebra of operators. When is constructed from a local field F with local ring , and , then is isomorphic to the convolution algebra of compactly supported bi-K-invariant functions on PGL(n+1,F). We give a proof, valid for any , that the multiplicative functionals on may all be expressed in terms of Hall–Littlewood polynomials. Regarding as a subalgebra of the C
*-algebra of bounded operators on the space of square summable functions on the vertex set of , we find the spectrum of the C
*-algebra , the closure of . This generalizes results obtained in [3] when n = 1 and in [5] when n = 2.
(Received 26 June 2000; in revised form 21 February 2001) 相似文献
20.
Marc Rosso 《Inventiones Mathematicae》1998,133(2):399-416
Let U
q
+ be the “upper triangular part” of the quantized enveloping algebra associated with a symetrizable Cartan matrix. We show
that U
q
+ is isomorphic (as a Hopf algebra) to the subalgebra generated by elements of degree 0 and 1 of the cotensor Hopf algebra
associated with a suitable Hopf bimodule on the group algebra of Z
n
. This method gives supersymetric as well as multiparametric versions of U
q
+ in a uniform way (for a suitable choice of the Hopf bimodule). We give a classification result about the Hopf algebras which
can be obtained in this way, under a reasonable growth condition. We also show how the general formalism allows to reconstruct
higher rank quantized enveloping algebras from U
q
sl(2) and a suitable irreducible finite dimensional representation.
Oblatum 21-III-1997 & 12-IX-1997 相似文献