共查询到20条相似文献,搜索用时 15 毫秒
1.
Akhlaq A. Siddiqui 《Archiv der Mathematik》2006,87(4):350-358
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
2.
3.
Let Z and W be JB*-triples and let T be a linear isometry from Z into W. For any z ∈ Z with ||z||<1, we show that Open image in new window if the Möbius transform induced by T(z) preserves the unit ball of T(Z). We show further that T is, locally, a triple homomorphism via a tripotent: for any z ∈ Z, there is a tripotent u in W** such that Open image in new window for all a, b, c in the smallest subtriple Z z of Z containing z, and also, {u,T(·),u}:Z z →W** is an isometry. 相似文献
4.
Antonio M. Peralta 《manuscripta mathematica》2001,105(2):265-281
In this paper we introduce 2-JB*-triple-summing operators on real and complex JB*-triples. These operators generalize 2-C*-summing operators on C*-algebras. We also obtain a Pietsch's factorization theorem in the setting of 2-JB*-triple-summing operators on JB*-triples.
Received: 18 December 2000 相似文献
5.
Antonio M. Peralta 《Mathematische Zeitschrift》2001,237(3):531-545
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
6.
Abstract. We describe the affine connections, geodesics and symmetries of various Banach manifolds of tripotents in JB*-triples which
include the C*-algebras and Hilbert spaces where the nonzero tripotents are respectively the partial isometries and the extreme
points of the closed unit ball.
Received July 7, 1998; in final form November 16, 1998 相似文献
7.
We prove that, if E is a real JB*-triple having a predual then is the unique predual of E and the triple product on E is separately $sigma (E,E_{*_{}})-$continuous. Received February 1, 1999; in final form March 29, 1999 / Published online May 8, 2000 相似文献
8.
Let A and B be C*-algebras. A linear map T : A → B is said to be a *-homomorphism at an element z ∈ A if ab* = z in A implies T (ab*) = T (a)T (b)* = T (z), and c*d = z in A gives T (c*d) = T (c)*T (d) = T (z). Assuming that A is unital, we prove that every linear map T : A → B which is a *-homomorphism at the unit of A is a Jordan *-homomorphism. If A is simple and infinite, then we establish that a linear map T : A → B is a *-homomorphism if and only if T is a *-homomorphism at the unit of A. For a general unital C*-algebra A and a linear map T : A → B, we prove that T is a *-homomorphism if, and only if, T is a *-homomorphism at 0 and at 1. Actually if p is a non-zero projection in A, and T is a ?-homomorphism at p and at 1 ? p, then we prove that T is a Jordan *-homomorphism. We also study bounded linear maps that are *-homomorphisms at a unitary element in A. 相似文献
9.
Ghislain Vaillant 《Integral Equations and Operator Theory》1995,22(3):339-351
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
10.
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
11.
Shanli Sun 《Linear algebra and its applications》2010,432(5):1337-1347
It is proved that a Jordan algebra of compact operators which is closed is either an Engel Jordan algebra, or contains a nonzero finite rank operator; Moreover, it is showed that any solvable Jordan algebra of compact operators on an infinite dimensional Banach space is triangularizable. 相似文献
12.
Bernard Aupetit 《Monatshefte für Mathematik》1998,125(3):179-187
In the first section we define the trace on the socle of a Jordan-Banach algebra in a purely spectral way and we prove that it satisfies several identities. In particular this trace defines the Faulkner bilinear form. In the second section, using analytic tools and the properties of the trace, we prove that a spectrum preserving linear mapping fromJ ontoJ
1, whereJ andJ
1 are semisimple Jordan-Banach algebras, is not far from being a Jordan isomorphism. It is in particular a Jordan isomorphism ifJ
1 is primitive with non-zero socle. 相似文献
13.
Let and be C*-dynamical systems and assume that is a separable simple C*-algebra and that α and β are *-automorphisms. Then the semicrossed products and are isometrically isomorphic if and only if the dynamical systems and are outer conjugate.
K. R. Davidson was partially supported by an NSERC grant. E. G. Katsoulis was partially supported by a summer grant from ECU 相似文献
14.
Wu Jing 《Quaestiones Mathematicae》2016,39(8):1037-1046
Let ? be an infinite dimensional complex Hilbert space and 𝒜 be a standard operator algebra on ? which is closed under the adjoint operation. We prove that every nonlinear *-Lie derivation δ of 𝒜 is automatically linear. Moreover, δ is an inner *-derivation. 相似文献
15.
16.
Laurent Marcoux 《Integral Equations and Operator Theory》1995,22(4):463-475
In this article we determine the closed Lie ideals of a uniformly hyperfiniteC
*-algebra, and of the tensor product of such an algebra withC(X), the space of continuous functions on a compact, Hausdorff space. This is done by localizing the Lie ideals in algebras of the form
, where
is an algebra over a field of characteristic not equal to 2.This research is partially supported by NSERC (Canada) 相似文献
18.
We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of unitary equivalence of automorphisms of a separable unital C*-algebra: Such relation is either smooth or not even classifiable by countable structures. 相似文献
19.
We study weak limits of the extreme points, ∂
e
(E
*
1), of the dual ball of a JB*-triple, E. We show that all such weak limits, except possibly the zero functional, are weak sequential limits and we discuss implications
for the structure of E.
Received: 9 April 2001 相似文献
20.
Further investigation into the properties of the Peirce-one space J1
corresponding to a weak*-closed inner ideal J in a JBW*-triple
A is carried out, and, in particular, it is shown that J1 contains
no non-trivial weak*-closed ideals.Received: 12 June 2002 相似文献