Projections in normed linear spaces and sufficient enlargements
نویسندگان
چکیده
منابع مشابه
Sufficient Enlargements in the Study of Projections in Normed Linear Spaces
The study of sufficient enlargements of unit balls of Banach spaces forms a natural line of attack of some well-known open problems of Banach space theory. The purpose of the paper is to present known results on sufficient enlargements and to state some open problems.
متن کامل2 00 2 Projections in Normed Linear Spaces and Sufficient Enlargements
Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists a projection P : Y → X such that P (B(Y)) ⊂ A (by B we denote the unit ball). The main purpose of the present paper is to continue investigation of sufficien...
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Let BY denote the unit ball of a normed linear space Y . A symmetric, bounded, closed, convex set A in a finite dimensional normed linear space X is called a sufficient enlargement for X if, for an arbitrary isometric embedding of X into a Banach space Y , there exists a linear projection P : Y → X such that P (BY ) ⊂ A. The main results of the paper: (1) Each minimal-volume sufficient enlargem...
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It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 1998
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s000130050270