共查询到20条相似文献,搜索用时 15 毫秒
1.
S. J. Bhatt 《Proceedings Mathematical Sciences》1998,108(3):283-303
A completely positive operator valued linear map ϕ on a (not necessarily unital) Banach *-algebra with continuous involution
admits minimal Stinespring dilation iff for some scalark > 0, ϕ(x)*ϕ(x) ≤ kϕ(x*x) for allx iff ϕ is hermitian and satisfies Kadison’s Schwarz inequality ϕ(h)
2
≤ kϕ(h
2) for all hermitianh iff ϕ extends as a completely positive map on the unitizationA
e
of A. A similar result holds for positive linear maps. These provide operator state analogues of the corresponding well-known
results for representable positive functionals. Further, they are used to discuss (a) automatic Stinespring representability
in Banach *-algebras, (b) operator valued analogue of Bochner-Weil-Raikov integral representation theorem, (c) operator valued
analogue of the classical Bochner theorem in locally compact abelian groupG, and (d) extendability of completely positive maps from *-subalgebras. Evans’ result on Stinespring respresentability in
the presence of bounded approximate identity (BAI) is deduced. A number of examples of Banach *-algebras without BAI are discussed
to illustrate above results. 相似文献
2.
Chmielinski has proved in the paper [4] the superstability of the generalized orthogonality equation |〈f(x), f(y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmielinski by proving a theorem: LetD
n be a suitable subset of ℝn. If a function f:D
n → ℝn satisfies the inequality ∥〈f(x), f(y)〉| |〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ D
n, thenf satisfies the generalized orthogonality equation for anyx, y ∈ D
n. 相似文献
3.
Kaidi El Amin Antonio Morales Campoy Angel Rodríguez Palacios 《manuscripta mathematica》2001,104(4):467-478
We characterize C
*-algebras as those complete normed associative complex algebras having approximate units bounded by one and whose open unit
balls are bounded symmetric domains. Such a characterization follows from the more general fact, also proved in the paper,
that non-commutative JB
*-algebras coincide with complete normed (possibly non-associative) complex algebras having approximate units bounded by one
and whose open unit balls are bounded symmetric domains.
Received: 3 October 2000 / Revised version: 26 January 2001 相似文献
4.
Michael Puschnigg 《Geometric And Functional Analysis》2010,20(1):243-259
We present a new construction of dense, isospectral subalgebras of unconditional Banach algebras over word-hyperbolic groups.
We study the algebras thus obtained and derive applications to delocalized L
2-invariants of closed Riemannian manifolds of negative curvature and to the local cyclic cohomology of the reduced group C*-algebras of word-hyperbolic groups. 相似文献
5.
Hvedri Inassaridze 《K-Theory》2000,21(1):25-56
Quillen's algebraic K-theory of discrete rings is extended to the category of normed algebras over a commutative Banach ring k with unit and its relationship with topological K-theory is established. Sufficient conditions for the isomorphism of algebraic and topological K-groups on the category of real normed algebras are given. The isomorphism of algebraic and topological K-functors on the category of polynomial extensions of stable C-algebras is proved. 相似文献
6.
Chun-Gil Park 《Acta Appl Math》2003,77(2):125-161
The paper is a survey on the Hyers–Ulam–Rassias stability of linear functional equations in Banach modules over a C
*-algebra. Its contents is divided into the following sections: 1. Introduction; 2. Stability of the Cauchy functional equation in Banach modules; 3. Stability of the Jensen functional equation in Banach modules; 4. Stability of the Trif functional equation in Banach modules; 5. Stability of cyclic functional equations in Banach modules over a C
*-algebra; 6. Stability of cyclic functional equations in Banach algebras and approximate algebra homomorphisms; 7. Stability of algebra *-homomorphisms between Banach *-algebras and applications. 相似文献
7.
Peter Šemrl 《Aequationes Mathematicae》1986,31(1):184-190
LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxX. 相似文献
8.
Summary The problem considered is that of maximizing
dt subject to x=G(x, y), x(0)=c, and0 ≤y≤x. An essentially new feature is determining in what regions y=x,0<y<x, and y=0. 相似文献
9.
Given a C*-normed algebra A which is either a Banach *-algebra or a Frechet *-algebra, we study the algebras Ω∞
A and Ωε
A obtained by taking respectively the projective limit and the inductive limit of Banach *-algebras obtained by completing
the universal graded differential algebra Ω*A of abstract non-commutative differential forms over A. Various quantized integrals on Ω∞
A induced by a K-cycle on A are considered. The GNS-representation of Ω∞
A defined by a d-dimensional non-commutative volume integral on a d
+-summable K-cycle on A is realized as the representation induced by the left action of A on Ω*A. This supplements the representation A on the space of forms discussed by Connes (Ch. VI.1, Prop. 5, p. 550 of [C]). 相似文献
10.
Jie Meng 《Semigroup Forum》1995,50(1):89-96
Chan and Shum [2] introduced the notion of implicative semigroups and obtained some of its important properties. BCK algebras
with condition (S) were introduced by Iséki [4] and extensively investigated by several authors. In this note, we prove that
implicative commutative semigroups are equivalent to BCK algebras with condition (S), that is, given an algebra <S;≤,·,*,1> of type (2,2,0), define ⊗ by stipulatingx⊗y=y*x and ≺ by puttingx≺y if and only ify≤x, then <S≤,·,*,1> is an implicative commutative semigroup if and only if <S;≺,·,⊗, 1> is a BCK algebra with condition (S); a nonempty subsetF ofS is an ordered filter of <S;≤,·,*, 1> if and only ifF is an ideal of <S;≺,·, ⊗, 1>.
The author would like to thank the referee for his valuable comments which helped in the modification of this paper. 相似文献
11.
Pavel Shvartsman 《Journal of Geometric Analysis》2002,12(2):289-324
We prove a Helly-type theorem for the family of all m-dimensional convex compact subsets of a Banach space X. The result is
formulated in terms of Lipschitz selections of set-valued mappings from a metric space (M, ρ) into this family.
Let M be finite and let F be such a mapping satisfying the following condition: for every subset M′ ⊂ M consisting of at most
2m+1 points, the restriction F|M′ of F to M′ has a selection fM′ (i. e., fM′(x) ∈ F(x) for all x ∈ M′) satisfying the Lipschitz condition ‖ƒM′(x) − ƒM′(y)‖X ≤ ρ(x, y), x, y ∈ M′. Then F has a Lipschitz selection ƒ: M → X such that ‖ƒ(x) − ƒ(y)‖X ≤ γρ(x,y), x, y ∈ M where γ is a constant depending only on m and the cardinality of M. We prove that in general, the upper
bound of the number of points in M′, 2m+1, is sharp.
If dim X = 2, then the result is true for arbitrary (not necessarily finite) metric space. We apply this result to Whitney’s
extension problem for spaces of smooth functions. In particular, we obtain a constructive necessary and sufficient condition
for a function defined on a closed subset of
R
2
to be the restriction of a function from the Sobolev space W
∞
2
(R
2).A similar result is proved for the space of functions on
R
2
satisfying the Zygmund condition. 相似文献
12.
Klaus Thomsen 《K-Theory》1991,4(3):245-267
We show that the homotopy groups of the group of quasi-unitaries inC
*-algebras form a homology theory on the category of allC
*-algebras which becomes topologicalK-theory when stabilized. We then show how this functorial setting, in particular the half-exactness of the involved functors, helps to calculate the homotopy groups of the group of unitaries in a series ofC
*-algebras. The calculations include the case of all AbelianC
*-algebras and allC
*-algebras of the formAB, whereA is one of the Cuntz algebras On n=2, 3, ..., an infinite dimensional simpleAF-algebra, the stable multiplier or corona algebra of a-unitalC
*-algebra, a properly infinite von Neumann algebra, or one of the projectionless simpleC
*-algebras constructed by Blackadar. 相似文献
13.
Reinhard Wolf 《Israel Journal of Mathematics》1999,110(1):125-151
The average distance theorem of Gross implies that for each realN-dimensional Banach space (N≥2) there is a unique positive real numberr(E) with the following property: For each positive integern and for all (not necessarily distinct)x
1,x
2, …,x
n inE with ‖x
1‖=‖x
2‖=…=‖x
n‖=1, there exists anx inE with ‖x‖=1 such that
The main result of this paper shows, thatr(E)≤2−1/N for each realN-dimensional Banach spaceE (N≥2) with the so-called quasihypermetric property (which is equivalent toE isL
1-embeddable). Moreover, equality holds if and only ifE is isometrically isomorphic to ℝ
N
equipped with the usual 1-norm. 相似文献
14.
Ralph deLaubenfels 《Semigroup Forum》1990,41(1):83-95
LetA be a linear operator on a Banach space. We consider when the following holds. (*)u′(t,x)=A(u(t,x)) (t≥0),u(0,x)=x, has a unique solution, for allx in the domain ofA
n+1
.
We discuss the relationship between (*), integrated semigroups, and C-semigroups. We use this to obtain new results about
integrated semigroups and the abstract Cauchy problem.
We give several examples where (*) may be easily shown using C-semigroups. Many of these examples may not be done directly
using integrated semigroups. 相似文献
15.
We consider some functional Banach algebras with multiplications as the usual convolution product * and the so‐called Duhamel product ?. We study the structure of generators of the Banach algebras (C(n)[0, 1], *) and (C(n)[0, 1], ?). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space Lp[0, 1] by the formula (Cφf)(x) = f(φ(x)). 相似文献
16.
It is proved that the equation (x
2−1)(y
2−1)=(z
2−1)2, |x|≠|y|, |z|≠1, is not solvable in integersx,y,z under the conditionx−y=kz, wherek is a positive integer different from 2.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 181–187, August, 1999. 相似文献
17.
W. M. Ruess 《Semigroup Forum》1995,51(1):335-341
For aC
0-contraction semigroup (S(t))
t≥0 of bounded linear operators on a complex Banach spaceX, J. A. Goldstein and B. Nagy [6] have shown that, givenx∈X, S(t)x=e
iλt
x, t≥0, for some λ∈ℝ, provided lim
t→∞
|<S(t)x,x
*
>|=|<x,x
*
>| for allx
*∈X*. We present (a) an extension to the case of nonlinear nonexpansive mapsS(t), t≥0, and (b) various generalizations in the linear context. 相似文献
18.
本文研究了对任意厄米实Banach*-代数的表示理论进行系统研究. 利用对该类代数所定义的一般态空间展开讨论. 获得了该类代数上可表示泛函的一系列好的性质,进而给出了不可约表示的等价刻画.这些结果将Naimark、Gaur等人的工作进行了推广. 相似文献
19.
Robert S. Strichartz 《Journal of Geometric Analysis》1991,1(3):269-289
Let μ be a measure on ℝn that satisfies the estimate μ(B
r(x))≤cr
α for allx ∈ ℝn and allr ≤ 1 (B
r(x) denotes the ball of radius r centered atx. Let ϕ
j,k
(ɛ)
(x)=2
nj2ϕ(ɛ)(2
j
x-k) be a wavelet basis forj ∈ ℤ, κ ∈ ℤn, and ∈ ∈E, a finite set, and letP
j
(T)=Σɛ,k
<T,ϕ
j,k
(ɛ)
>ϕ
j,k
(ɛ)
denote the associated projection operators at levelj (T is a suitable measure or distribution). Iff ∈Ls
p(dμ) for 1 ≤p ≤ ∞, we show thatP
j(f dμ) ∈ Lp(dx) and ||P
j
(fdμ)||L
p(dx)≤c2
j((n-α)/p′))||f||L
p(dμ) for allj ≥ 0. We also obtain estimates for the limsup and liminf of ||P
j
(fdμ)||L
p(dx) under more restrictive hypotheses.
Communicated by Guido Weiss 相似文献
20.
Soon-Mo Jung Byungbae Kim 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):293-308
A result of Skof and Terracini will be generalized; More precisely, we will prove that if a functionf : [-t, t]n →E satisfies the inequality (1) for some δ > 0 and for allx, y ∈ [-t, t]n withx + y, x - y ∈ [-t, t]n, then there exists a quadratic functionq: ℝn →E such that ∥f(x) -q(x)∥ < (2912n2 + 1872n + 334)δ for anyx ∈ [-t, t]
n
. 相似文献