کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598974 1631111 2015 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Commutators, commutativity and dimension in the socle of a Banach algebra: A generalized Wedderburn–Artin and Shoda's theorem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Commutators, commutativity and dimension in the socle of a Banach algebra: A generalized Wedderburn–Artin and Shoda's theorem
چکیده انگلیسی

As a follow-up to work done in [7], some new insights to the structure of the socle of a semisimple Banach algebra are obtained. In particular, it is shown that the socle is isomorphic as an algebra to the direct sum of tensor products of corresponding left and right minimal ideals. Remarkably, the finite-dimensional case here reduces to the classical Wedderburn–Artin Theorem, and this approach does not use any continuous irreducible representations of the algebra in question. Furthermore, the structure of the socles for which the classical Shoda's Theorem for matrices can be extended, is characterized exactly as those socles which are minimal two-sided ideals. It is then shown that the set of commutators in the socle (i.e. {xy−yx:x,y∈SocA}) is a vector subspace. Finally, we characterize those socles which belong to the center of a Banach algebra and obtain results which suggest that the dimension of certain subalgebras of the socle in fact provides a measure, to some extent, of commutativity.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 484, 1 November 2015, Pages 175–198
نویسندگان
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