کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9495969 | 1335204 | 2005 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Duality and operator algebras: automatic weak* continuity and applications
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras, and give several applications of the surprising fact that certain maps are always weak*-continuous on dual spaces. In particular, if X is a subspace of a C*-algebra A, and if aâA satisfies aXâX, then we show that the function xâ¦ax on X is automatically weak* continuous if either (a) X is a dual operator space, or (b) a*XâX and X is a dual Banach space. These results hinge on a generalization to Banach modules of Tomiyama's famous theorem on contractive projections onto a C*-subalgebra. Applications include a new characterization of the Ï-weakly closed (possibly nonunital and nonselfadjoint) operator algebras, and a generalization of the theory of W*-modules to the framework of modules over such algebras. We also give a Banach module characterization of Ï-weakly closed spaces of operators which are invariant under the action of a von Neumann algebra.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 224, Issue 2, 15 July 2005, Pages 386-407
Journal: Journal of Functional Analysis - Volume 224, Issue 2, 15 July 2005, Pages 386-407
نویسندگان
David P. Blecher, Bojan Magajna,