Paths between Banach spaces
نویسندگان
چکیده
منابع مشابه
Distances between Banach spaces
Abstraca. The main object of the paper is to study the distance betwecn Banach spaces introduced by Kadets. For Banach spaccs Xand y. thc lGders distancc is denned to be rhe infimum of the Hausdorfl distance d(Bx, rr) betwecn the respoctive closed unit balls over all isomctric linear embeddings of f and yinto a common Banach space Z. This is comparcd with the Gromov-Hausdorff distance which is ...
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Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...
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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...
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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: Glasgow Mathematical Journal
سال: 2002
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089502020074