Boundaries and polyhedral Banach spaces

نویسندگان
چکیده

منابع مشابه

A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

Let (xn) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that

متن کامل

Boundaries for Algebras of Holomorphic Functions on Banach Spaces

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space X is the unit sphere SX if X is locally c-convex. In particular, it is shown that the unit sphere of the OrliczLorentz sequence space λφ,w i...

متن کامل

Banach Spaces and Hilbert Spaces

A sequence {vj} is said to be Cauchy if for each > 0, there exists a natural number N such that ‖vj−vk‖ < for all j, k ≥ N . Every convergent sequence is Cauchy, but there are many examples of normed linear spaces V for which there exists non-convergent Cauchy sequences. One such example is the set of rational numbers Q. The sequence (1.4, 1.41, 1.414, . . . ) converges to √ 2 which is not a ra...

متن کامل

Proximinality properties in Lp (μ,X) and polyhedral direct sums of Banach spaces

For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. Let (P) be either proximinality or strong 1 1 2 -ball property and if (P) is separably determined for Y in X, then we prove that L1(μ, Y ) has the same property (P) in L1(μ,X). For an M -embedded space X, we give a class of elements in L1(μ,X ∗∗) having best approximations from L1(μ,X). We also pr...

متن کامل

Banach Spaces

(A revised and expanded version of these notes are now published by Springer.) 1 Banach Spaces Definition A normed vector space X is a vector space over R or C with a function called the norm. 1. The set of real numbers with the norm taken to be the absolute value.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2015

ISSN: 0002-9939,1088-6826

DOI: 10.1090/proc/12644