Results 21 to 30 of about 128 (122)
Double‐dual n‐types over Banach spaces not containing ℓ1
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 33, Page 1747-1755, 2004., 2004 Let E be a Banach space. The concept of n‐type overE is introduced here, generalizing the concept of type overE introduced by Krivine and Maurey. Let E″ be the second dual of E and fix g″1,…g″n∈E″. The function τ : E × ℝn → ℝ, defined by letting τ(x,a1,…,an)=‖x+∑i=1naig″i‖ for all x ∈ E and all a1, …, an ∈ ℝ, defines an n‐type over E. Types that can be
Markus Pomper
wiley +1 more source
On uniform Kadec‐Klee properties and rotundity in generalized Cesàro sequence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 2, Page 91-97, 2004., 2004 We consider the generalized Cesàro sequence spaces defined by Suantai (2003) and consider it equipped with the Amemiya norm. The main purpose of this paper is to show that ces(p) equipped with the Amemiya norm is rotund and has uniform Kadec‐Klee property.
Narin Petrot, Suthep Suantai
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Strong and weak convergence of Ishikawa iterations for best proximity pairs
Open Mathematics, 2020 Let A and B be nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to be a noncyclic relatively nonexpansive mapping if T(A) ⊆ A, T(B) ⊆ B and ∥Tx − Ty∥ ≤ ∥x − y∥ for all (x, y) ∈ A × B.
Gabeleh Moosa +3 more
doaj +1 more source
Small sets in best approximation theory
, 2010 Best approximation, Metric projection, Well-posedness, Baire category, Porous sets, Cone supported sets, 41A65, 46B20,
J. P. Revalski +3 more
core +1 more source
On the weak uniform rotundity of Banach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 30, Page 1943-1945, 2003., 2003 We prove that if Xi, i = 1, 2, …, are Banach spaces that are weak* uniformly rotund, then their lp product space (p > 1) is weak* uniformly rotund, and for any weak or weak* uniformly rotund Banach space, its quotient space is also weak or weak* uniformly rotund, respectively.
Wen D. Chang, Ping Chang
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Some results about Lipschitz p-Nuclear Operators
Moroccan Journal of Pure and Applied Analysis, 2021 The aim of this paper is to study the onto isometries of the space of strongly Lipschitz p-nuclear operators, introduced by D. Chen and B. Zheng (Nonlinear Anal.,75, 2012).
Bey Khedidja, Belacel Amar
doaj +1 more source
Proximinal subspaces of A(K) of finite codimension
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 39, Page 2501-2505, 2003., 2003 We study an analogue of Garkavi′s result on proximinal subspaces of C(X) of finite codimension in the context of the space A(K) of affine continuous functions on a compact convex set K. We give an example to show that a simple‐minded analogue of Garkavi′s result fails for these spaces.
T. S. S. R. K. Rao
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On k‐nearly uniform convex property in generalized Cesàro sequence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 57, Page 3599-3607, 2003., 2003 We define a generalized Cesàro sequence space ces(p), where p = (pk) is a bounded sequence of positive real numbers, and consider it equipped with the Luxemburg norm. The main purpose of this paper is to show that ces(p) is k‐nearly uniform convex (k‐NUC) for k ≥ 2 when limn→∞infpn > 1. Moreover, we also obtain that the Cesàro sequence space cesp(where
Winate Sanhan, Suthep Suantai
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Tight Embeddability of Proper and Stable Metric Spaces
Analysis and Geometry in Metric Spaces, 2015 We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We
Baudier F., Lancien G.
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DP1 and completely continuous operators
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 37, Page 2375-2378, 2003., 2003 W. Freedman introduced an alternate to the Dunford‐Pettis property, called the DP1 property, in 1997. He showed that for 1 ≤ p < ∞, (⊕α∈𝒜Xα) p has the DP1 property if and only if each Xα does. This is not the case for (⊕α∈𝒜Xα) ∞. In fact, we show that (⊕α∈𝒜Xα) ∞ has the DP1 property if and only if it has the Dunford‐Pettis property.
Elizabeth M. Bator, Dawn R. Slavens
wiley +1 more source