کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616914 1339363 2013 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
How does the distortion of linear embedding of C0(K) into C0(Γ,X) spaces depend on the height of K?
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
How does the distortion of linear embedding of C0(K) into C0(Γ,X) spaces depend on the height of K?
چکیده انگلیسی
Let C0(K) denote the space of all continuous scalar-valued functions defined on the locally compact Hausdorff space K which vanish at infinity, provided with the supremum norm. Let Γ be an infinite set endowed with discrete topology and X a Banach space. We denote by C0(Γ,X) the Banach space of X-valued functions defined on Γ which vanish at infinity, provided with the supremum norm. In this paper, we prove that, if X has non-trivial cotype and there exists a linear isomorphism T from C0(K) into C0(Γ,X), then K has finite height ht(K), and the distortion ‖T‖‖T−1‖ is greater than or equal to 2ht(K)−1. The statement of this theorem is optimal and improves a 1970 result of Gordon.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 402, Issue 1, 1 June 2013, Pages 185-190
نویسندگان
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