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1.
We study transitivity conditions on the norm of JB *-triples, C *-algebras, JB-algebras, and their preduals. We show that, for the predual X of a JBW *-triple, each one of the following conditions i) and ii) implies that X is a Hilbert space. i) The closed unit ball of X has some extreme point and the norm of X is convex transitive. ii) The set of all extreme points of the closed unit ball of X is non rare in the unit sphere of X. These results are applied to obtain partial affirmative answers to the open problem whether every JB *-triple with transitive norm is a Hilbert space. We extend to arbitrary C *-algebras previously known characterizations of transitivity [20] and convex transitivity [36] of the norm on commutative C *-algebras. Moreover, we prove that the Calkin algebra has convex transitive norm. We also prove that, if X is a JB-algebra, and if either the norm of X is convex transitive or X has a predual with convex transitive norm, then X is associative. As a consequence, a JB-algebra with almost transitive norm is isomorphic to the field of real numbers. Received: 9 June 1999 / Revised version: 20 February 2000  相似文献   

2.
We prove that given a real JB*-triple E, and a real Hilbert space H, then the set of those bounded linear operators T from E to H, such that there exists a norm one functional and corresponding pre-Hilbertian semi-norm on E such that for all , is norm dense in the set of all bounded linear operators from E to H. As a tool for the above result, we show that if A is a JB-algebra and is a bounded linear operator then there exists a state such that for all . Received June 28, 1999; in final form January 28, 2000 / Published online March 12, 2001  相似文献   

3.
We prove that x is in the norm closure of invertibles whenever x is self-adjoint in some unitary isotope of a JB*-algebra. In the sequel, we investigate certain links between the elements of the unit ball which are self-adjoint in some unitary isotope of a JB*-algebra and the elements which are average of two unitaries. Received: 9 September 2005  相似文献   

4.
We prove that every generalized Jordan derivation D from a JB?-algebra 𝒜 into itself or into its dual space is automatically continuous. In particular, we establish that every generalized Jordan derivation from a C?-algebra to a Jordan Banach module is continuous. As a consequence, every generalized derivation from a C?-algebra to a Banach bimodule is continuous.  相似文献   

5.
We prove the Thom isomorphism theorem for the K-theory of bundles with fibers equal to a projective module over a C*-algebra for the action of a compact Lie group both on this algebra and on the total space. Bibliography: 12 titles.  相似文献   

6.
V. Pták's inequality is valid for every hermitian completeQ locallym-convex (:l.m.c.) algebra. Every algebra of the last kind is, in particular, symmetric. Besides, a (Hausdorff) locallyC *-algebra (being always symmetric) with the propertyQ is, within a topological algebraic isomorphism, aC *-algebra. Furthermore, a type of Raikov's criterion for symmetry is also valid for non-normed topological*-algebras. Concerning topological tensor products, one gets that symmetry of the-completed tensor product of two unital Fréchet l.m.c.*-algebrasE, F ( denotes the projective tensorial topology) is always passed toE, F, while the converse occurs when moreover either ofE, F is commutative.  相似文献   

7.
We establish the equivalence of the following three properties of a -algebra A. (a) Every positive elementary operator on A is completely positive. (b) The norm and the cb-norm coincide for every elementary operator on A. (c) A is an extension of an antiliminal -algebra by an abelian one. Received: 15 July 1998 / in revised form: 22 September 1998  相似文献   

8.
Unbounded C*-seminorms generated by families of biweights on a partial *-algebra are considered and the admissibility of biweights is characterized in terms of unbounded C*-seminorms they generate. Furthermore, it is shown that, under suitable assumptions, when the family of biweights consists of all those ones which are relatively bounded with respect to a given C*-seminorm q, it can be obtained an expression for q analogous to that one which holds true for the norm of a C*-algebra.  相似文献   

9.
We discuss the representation theory of both the locally convex and non-locally convex topological*-algebras. First we discuss the*-representation of topological*-algebras by operators on a Hilbert space. Then we study those topological*-algebras so that every*-representation of which on a Hilbert space is necessarily continuous. It is well-known that each*-representation of aB *-algebra on a Hilbert space is continuous. We show that this is true for a large class of*-algebras more general thanB *-algebras, including certain non-locally convex*-algebras. Finally, we investigate the conditions under which a positive functional on a topological*-algebra is representable.The research of the first-named author was partially supported by an NSERC grant. This work was done by the second-named author when he was a post-doctoral fellow at McMaster University.  相似文献   

10.
In this note we show that a separable C*-algebra is nuclear and has a quasidiagonal extension by (the ideal of compact operators on an infinite-dimensional separable Hilbert space) if and only if it is anuclear finite algebra (NF-algebra) in the sense of Blackadar and Kirchberg, and deduce that every nuclear C*-subalgebra of aNF-algebra isNF. We show that strongNF-algebras satisfy a Følner type condition.  相似文献   

11.
Let A be a unitary commutative complete locally m-convex C *-algebra. We prove that the projective finitely generated A-modules admit differentiable A-valued bump-functions. Then we consider manifolds modelled on such modules and we prove that locally defined differentiable mappings and sections on these manifolds extend to global ones. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

12.
A pro-C*-algebra is a (projective) limit of C*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C*-algebras can be seen as non-commutative k-spaces. An element of a pro-C*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C*-algebra. In this paper, we investigate pro-C*-algebras from a categorical point of view. We study the functor (−) b that assigns to a pro-C*-algebra the C*-algebra of its bounded elements, which is the dual of the Stone-Čech-compactification. We show that (−) b is a coreflector, and it preserves exact sequences. A generalization of the Gelfand duality for commutative unital pro-C*-algebras is also presented.  相似文献   

13.
We prove that the Cox ring of the projectivization P(?) of a rank two toric vector bundle ?, over a toric variety X, is a finitely generated k-algebra. As a consequence, P(?) is a Mori dream space if the toric variety X is projective and simplicial.  相似文献   

14.
We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on ℓ2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w * closure of the set of its points of Gateaux differentiability is norm separable. Received May 31, 1999 / final version received February 16, 2000?Published online April 19, 2000  相似文献   

15.
《Quaestiones Mathematicae》2013,36(2):265-274
We impose a condition on a commutative regular Fréchet algebra (A, (pm )) to ensure that A/kerpm is a Fréchet Q-algebra. This implies that if θ is an n-homomorphism on certain Fréchet algebras (A, (pm )) into semisimple commutative Fréchet algebras (B,(qm)) such that θ(kerpm) ? kerqm, for large enough m, then θ is continuous. We also show that if A is a Fréchet Q-algebra, B is a semisimple Fréchet algebra, θ: AB is a dense range n-homomorphism such that θ(A) is factorizable, and the spectral radius vB is continuous on the separating space (θ), then θ is automatically continuous.  相似文献   

16.
SupposeM is a von Neumann algebra on a Hilbert spaceH andI is any norm closed ideal inM. We extend to this setting the well known fact that the compact operators on a Hilbert space are precisely those whose restrictions to the closed unit ball are weak to norm continuous.  相似文献   

17.
It is proved that any non-archimedean non-normable Fréchet space with a Schauder basis and a continuous norm has a quotient without the bounded approximation property. It follows that any infinite-dimensional non-archimedean Fréchet space, which is not isomorphic to any of the following spaces: , has a quotient without a Schauder basis. Clearly, any quotient of c0 and has a Schauder basis. It is shown a similar result for and  相似文献   

18.
Many structures in functional analysis are introduced as the limit of an inverse (aka projective) system of seminormed spaces [2, 3, 8]. In these situations, the dual is moreover equipped with a seminorm. Although the topology of the inverse limit is seldom metrizable, there is always a natural overlying locally convex approach structure. We provide a method for computing the adjoint of this space, by showing that the dual of a limit of locally convex approach spaces becomes a co-limit in the category of seminormed spaces. As an application we obtain an isometric representation of the dual space of real valued continuous functions on a locally compact Hausdorff space X, equipped with the compact open structure.  相似文献   

19.
We give a short answer to the question in the title: dendrits. Precisely we show that the C*-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category C1 of all (not necessarily commutative) unital C*-algebras if and only if X is an absolute retract of dimension dimX?1 or, equivalently, that X is a dendrit.  相似文献   

20.
Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebraA with a fixed projectionp. The resulting spaceP(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invertible group ofA. Moreover, several metrics (chordal, spherical, pseudo-chordal, non-Euclidean-in Schwarz-Zaks terminology) are considered, allowing a comparison amongP(p), the Grassmann manifold ofA and the space of positive elements which are unitary with respect to the bilinear form induced by the reflection =2p–1. Among several metrical results, we prove that geodesics are unique and of minimal length when measured with the spherical and non-Euclidean metrics.Partially supported by UBACYT TW49 and TX92, PIP 4463 (CONICET) and ANPCYT PICT 97-2259 (Argentina)  相似文献   

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