A universal differentiability set in Banach spaces with separable dual

被引：11

作者：

Dore, Michael ^{[1
]}

Maleva, Olga ^{[1
]}

机构：

[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2011年 / 261卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Universal differentiability set; Frechet differentiability; Null set; FRECHET DIFFERENTIABILITY; LIPSCHITZ FUNCTIONS; POINTS;

D O I：

10.1016/j.jfa.2011.05.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Frechet differentiable somewhere in S. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1674 / 1710

页数：37

共 50 条

[11] NON-EXISTENCE OF A SEPARABLE REFLEXIVE BANACH SPACE UNIVERSAL FOR ALL SEPARABLE REFLEXIVE BANACH SPACES
SZLENK, W
STUDIA MATHEMATICA, 1968, 30 (01) : 53 - &
[12] A NOTE ON SEPARABLE BANACH-SPACES WITH NONSEPARABLE DUAL
HAGLER, JN
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 99 (03) : 452 - 454
[13] SEPARABLE BANACH SPACES CONTAINING ALL SEPARABLE REFLEXIVE BANACH SPACES
WOJTASZCAZYK, P
STUDIA MATHEMATICA, 1971, 37 (02) : 197 - +
[14] On the differentiability of norms in Banach spaces
Felipe Munoz-Tello, Andres
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (02): : 2015 - 2023
[15] Operator ranges in Banach spaces with weak star separable dual
Jimenez-Sevilla, Mar
Lajara, Sebastian
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 531 (02)
[16] Banach spaces with separable duals support dual hypercyclic operators
Salas, Hector N.
GLASGOW MATHEMATICAL JOURNAL, 2007, 49 : 281 - 290
[17] SEPARABLE UNIVERSAL BANACH LATTICES
Leung, Denny H.
Li, Lei
Oikhberg, Timur
Tursi, Mary Angelica
ISRAEL JOURNAL OF MATHEMATICS, 2019, 230 (01) : 141 - 152
[18] Separable universal Banach lattices
Denny H. Leung
Lei Li
Timur Oikhberg
Mary Angelica Tursi
Israel Journal of Mathematics, 2019, 230 : 141 - 152
[19] Gateaux Differentiability of Convex Functions and Weak Dentable Set in Nonseparable Banach Spaces
Shang, Shaoqiang
Cui, Yunan
JOURNAL OF FUNCTION SPACES, 2019, 2019
[20] On set differential equations in Banach spaces - a second type Hukuhara differentiability approach
Malinowski, Marek T.
APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (01) : 289 - 305

← 1 2 3 4 5 →