منابع مشابه
On Bilipschitz Extensions in Real Banach Spaces
and Applied Analysis 3 (3) k D (z 1 , z 2 ) ≤ c 1 log(1+|z 1 −z 2 |/min{d D (z 1 ), d D (z 2 )})+ d for all z 1 , z 2 ∈ D. Gehring and Palka [14] introduced the quasihyperbolic metric of a domain in R, and it has been recently used by many authors in the study of quasiconformal mappings and related questions [16]. In the case of domains in R, the equivalence of items (1) and (3) in Theorem E ...
متن کاملQuantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces
We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of H...
متن کاملBanach 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 کاملBanach Spaces
Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/fun/notes 2012-13/05 banach.pdf] 1. Basic definitions 2. Riesz’ Lemma 3. Counter-example: non-existence of norm-minimizing element 4. Normed spaces of continuous linear maps 5. Dual spaces of normed spaces 6. Banach-Steinhaus/uniform-boundedness theorem 7. Open mapping theore...
متن کاملBanach 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...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2004
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2004.02.012