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Titlebook: Similarity Problems and Completely Bounded Maps; Gilles Pisier Book 2001Latest edition Springer-Verlag Berlin Heidelberg 2001 Algebra.Comp

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發(fā)表于 2025-3-21 19:03:53 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Similarity Problems and Completely Bounded Maps
編輯Gilles Pisier
視頻videohttp://file.papertrans.cn/868/867394/867394.mp4
概述Two chapters have been added on the HALMOS and KADISON similarity problems.Includes supplementary material:
叢書(shū)名稱(chēng)Lecture Notes in Mathematics
圖書(shū)封面Titlebook: Similarity Problems and Completely Bounded Maps; Gilles Pisier Book 2001Latest edition Springer-Verlag Berlin Heidelberg 2001 Algebra.Comp
描述These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities.
出版日期Book 2001Latest edition
關(guān)鍵詞Algebra; Completely bounded representation; H (p) spaces; Harmonic analysis; Hilbert space; Polynomially
版次2
doihttps://doi.org/10.1007/b55674
isbn_softcover978-3-540-41524-4
isbn_ebook978-3-540-44563-0Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2001
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沙發(fā)
發(fā)表于 2025-3-21 23:37:15 | 只看該作者
板凳
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Subject and Notation Index,Abstract not available.
地板
發(fā)表于 2025-3-22 06:33:48 | 只看該作者
Gilles PisierTwo chapters have been added on the HALMOS and KADISON similarity problems.Includes supplementary material:
5#
發(fā)表于 2025-3-22 10:05:04 | 只看該作者
Lecture Notes in Mathematicshttp://image.papertrans.cn/s/image/867394.jpg
6#
發(fā)表于 2025-3-22 16:38:41 | 只看該作者
https://doi.org/10.1007/b55674Algebra; Completely bounded representation; H (p) spaces; Harmonic analysis; Hilbert space; Polynomially
7#
發(fā)表于 2025-3-22 20:53:54 | 只看該作者
8#
發(fā)表于 2025-3-22 21:56:56 | 只看該作者
8. Completely bounded maps in the Banach space setting,etting, we extend the fundamental factorization of c.b. maps. We show that the extension property still holds under suitable assumptions. Finally, we apply these results to the similarity problem for homomorphisms in this broader framework.
9#
發(fā)表于 2025-3-23 02:58:45 | 只看該作者
9. The Sz.-Nagy-Halmos similarity problem,tor on Hilbert space which is not similar to a contraction. We also include two related finite dimensional estimates related to . x .-matrices. For one of them, the estimate for polynomially bounded . x .-matrices, the sharp order of growth, when . tends to infinity, is not yet known.
10#
發(fā)表于 2025-3-23 08:16:12 | 只看該作者
10. The Kadison Similarity Problem, different questions which appeared in other contexts: Arveson’s hyperreflexivity problem and Dixmier’s invariant opemtor range problem. Finally, we describe the author’s recent work on the notion of “l(fā)ength” of an opemtor algebm, which also leads to one more reformulation of Kadison’s question.
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