کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415209 1334972 2014 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Further properties of ℓp dimension
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Further properties of ℓp dimension
چکیده انگلیسی

This article establishes more properties of the ℓp dimension introduced in a previous article. Given an amenable group Γ acting by translation on ℓp(Γ), a number satisfying dimension-like properties is associated to the (usually infinite dimensional) subspaces Y of ℓp(Γ) which are invariant under the action of Γ. This may be interpreted as a von Neumann dimension for ℓp spaces. As a consequence, for p∈[1,2], if Y is a closed non-trivial Γ-invariant subspace of ℓp(Γ) and let Yn be an increasing sequence of closed Γ-invariant subspace such that ⋃Yn¯=ℓp(Γ;V), then there exist a k such that Yk∩Y≠{0}.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 266, Issue 2, 15 January 2014, Pages 487-513
نویسندگان
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