共查询到10条相似文献,搜索用时 109 毫秒
1.
Martin Mathieu 《Proceedings of the American Mathematical Society》2004,132(2):443-446
A linear mapping from a subspace of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant such that for all , where denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple -algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.
2.
Huaxin Lin 《Proceedings of the American Mathematical Society》2003,131(12):3813-3819
Let be a unital simple -algebra with real rank zero. It is shown that if satisfies a so-called fundamental comparison property, then has tracial topological rank zero. Combining some previous results, it is shown that a unital simple -algebra with real rank zero, stable rank one and weakly unperforated must have slow dimension growth.
3.
Applying the density theorem on algebras with -derivations, we show that if a -derivation of a unital Banach algebra is spectrally bounded, then . Also, if and only if , where denotes the spectral radius of .
4.
Fabio Nicola 《Proceedings of the American Mathematical Society》2003,131(9):2841-2848
We are concerned with the so-called -pseudo-differential calculus. We describe the spectrum of the unital and commutative -algebra given by the norm closure of the space of -order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their -theory is computed.
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6.
Fré dé ric Gourdeau B. E. Johnson Michael C. White 《Transactions of the American Mathematical Society》2005,357(12):5097-5113
Let be the unital semigroup algebra of . We show that the cyclic cohomology groups vanish when is odd and are one dimensional when is even (). Using Connes' exact sequence, these results are used to show that the simplicial cohomology groups vanish for . The results obtained are extended to unital algebras for some other semigroups of .
7.
Chun-Gil Park 《Proceedings of the American Mathematical Society》2004,132(6):1739-1745
It is shown that for an approximate algebra homomorphism on a Banach -algebra , there exists a unique algebra -homomorphism near the approximate algebra homomorphism. This is applied to show that for an approximate automorphism on a unital -algebra , there exists a unique automorphism near the approximate automorphism. In fact, we show that the approximate automorphism is an automorphism.
8.
Choonkil Park 《Mathematische Nachrichten》2008,281(3):402-411
Let X, Y be Banach modules over a C *‐algebra. We prove the Hyers–Ulam–Rassias stability of the following functional equation in Banach modules over a unital C *‐algebra: It is shown that a mapping f: X → Y satisfies the above functional equation and f (0) = 0 if and only if the mapping f: X → Y is Cauchy additive. As an application, we show that every almost linear bijection h: A → B of a unital C *‐algebra A onto a unital C *‐algebra B is a C *‐algebra isomorphism when h (2d uy) = h (2d u) h (y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
A. Chigogidze A. Karasev M. Rø rdam 《Proceedings of the American Mathematical Society》2004,132(3):783-788
It is proved that if is a compact Hausdorff space of Lebesgue dimension , then the squaring mapping , defined by , is open if and only if . Hence the Lebesgue dimension of can be detected from openness of the squaring maps . In the case it is proved that the map , from the selfadjoint elements of a unital -algebra into its positive elements, is open if and only if is isomorphic to for some compact Hausdorff space with .
10.
Raf Cluckers 《Transactions of the American Mathematical Society》2004,356(4):1489-1499
We prove a conjecture of Denef on parameterized -adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), the pieces being geometrically simple sets, called cells. We also classify subanalytic sets up to subanalytic bijection.