Differentiability and ball-covering property in Banach spaces

作者: Shaoqiang Shang

DOI: 10.1016/J.JMAA.2015.09.009

关键词:

摘要: Abstract In this paper, author proves that if X 1 and 2 are Gâteaux differentiable space, then have the ball-covering property only ( × , ‖ ⋅ p ) ∞ property, where x y = + ∈ [ max ⁡ { } .

参考文章(22)
Warren B. Moors, Sivajah Somasundaram, A Gâteaux differentiability space that is not weak Asplund Proceedings of the American Mathematical Society. ,vol. 134, pp. 2745- 2754 ,(2006) , 10.1090/S0002-9939-06-08402-4
Shaoqiang Shang, Yunan Cui, Locally $2$-uniform convexity and ball-covering property in Banach space Banach Journal of Mathematical Analysis. ,vol. 9, pp. 42- 53 ,(2015) , 10.15352/BJMA/09-1-4
Lixin Cheng, Marián Fabian, The product of a Gateaux differentiability space and a separable space is a Gateaux differentiability space Proceedings of the American Mathematical Society. ,vol. 129, pp. 3539- 3541 ,(2001) , 10.1090/S0002-9939-01-06252-9
LiXin Cheng, QingJin Cheng, XiaoYan Liu, Ball-covering property of Banach spaces that is not preserved under linear isomorphisms Science China-mathematics. ,vol. 51, pp. 143- 147 ,(2008) , 10.1007/S11425-007-0102-8
Shaoqiang Shang, Yunan Cui, Ball-Covering Property in Uniformly Non- Banach Spaces and Application Abstract and Applied Analysis. ,vol. 2013, pp. 1- 7 ,(2013) , 10.1155/2013/873943
D Preiss, Differentiability of Lipschitz functions on Banach spaces Journal of Functional Analysis. ,vol. 91, pp. 312- 345 ,(1990) , 10.1016/0022-1236(90)90147-D
John Giles, David Gregory, Brailey Sims, GEOMETRICAL IMPLICATIONS OF UPPER SEMI-CONTINUITY OF THE DUALITY MAPPING ON A BANACH SPACE Pacific Journal of Mathematics. ,vol. 79, pp. 99- 109 ,(1978) , 10.2140/PJM.1978.79.99
Zhonghao Zheng, Xiuchun Bi, Shuguang Zhang, Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion Abstract and Applied Analysis. ,vol. 2013, pp. 1- 11 ,(2013) , 10.1155/2013/564524
Lixin Cheng, BALL-COVERING PROPERTY OF BANACH SPACES Israel Journal of Mathematics. ,vol. 156, pp. 111- 123 ,(2006) , 10.1007/BF02773827