Weakly compact sets in Orlicz sequence spaces

2021 ◽  
pp. 1-14
Author(s):  
Siyu Shi ◽  
Zhongrui Shi ◽  
Shujun Wu
Keyword(s):  
Sequence Spaces ◽  
Compact Sets ◽  
Weakly Compact ◽  
Orlicz Sequence Spaces ◽  
Weakly Compact Sets

A Weak Hadamard Smooth Renorming of L1(Ω, μ)

1993 ◽  
Vol 36 (4) ◽  
pp. 407-413 ◽  
Author(s):  
Jonathan M. Borwein ◽  
Simon Fitzpatrick
Keyword(s):  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

AbstractWe show that L1(μ) has a weak Hadamard differential)le renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if μ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L1.

Weakly compact sets in L∞(μ,E)

2012 ◽  
Vol 263 (4) ◽  
pp. 1098-1102
Author(s):  
Surjit Singh Khurana
Keyword(s):  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

Banach Spaces that are Uniformly Rotund in Weakly Compact Sets of Directions

1977 ◽  
Vol 29 (5) ◽  
pp. 963-970 ◽  
Author(s):  
Mark A. Smith
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Nonzero Element ◽  
Bounded Subset ◽  
Compact Sets ◽  
Weakly Compact ◽  
Uniform Rotundity ◽  
Minimum Depth ◽  
Weakly Compact Sets

In a Banach space, the directional modulus of rotundity, δ (ϵ, z), measures the minimum depth at which the midpoints of all chords of the unit ball which are parallel to z and of length at least ϵ are buried beneath the surface. A Banach space is uniformly rotund in every direction (URED) if δ (ϵ, z) is positive for every positive ϵ and every nonzero element z. This concept of directionalized uniform rotundity was introduced by Garkavi [6] to characterize those Banach spaces in which every bounded subset has at most one Čebyšev center.

Pointwise compactness and weakly compact sets inL E ?

1981 ◽  
Vol 176 (1) ◽  
pp. 35-38
Author(s):  
Surjit Singh Khurana
Keyword(s):  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

scholarly journals Farthest points and the farthest distance map

2005 ◽  
Vol 71 (3) ◽  
pp. 425-433 ◽  
Author(s):  
Pradipta Bandyopadhyay ◽  
S. Dutta
Keyword(s):  
Banach Space ◽  
Maximal Monotone ◽  
Convex Banach Space ◽  
Closed Convex Hull ◽  
Compact Sets ◽  
Weakly Compact ◽  
Distance Map ◽  
Farthest Points ◽  
Bounded Set ◽  
Weakly Compact Sets

In this paper, we consider farthest points and the farthest distance map of a closed bounded set in a Banach space. We show, inter alia, that a strictly convex Banach space has the Mazur intersection property for weakly compact sets if and only if every such set is the closed convex hull of its farthest points, and recapture a classical result of Lau in a broader set-up. We obtain an expression for the subdifferential of the farthest distance map in the spirit of Preiss' Theorem which in turn extends a result of Westphal and Schwartz, showing that the subdifferential of the farthest distance map is the unique maximal monotone extension of a densely defined monotone operator involving the duality map and the farthest point map.

scholarly journals Weakly compact sets and smooth norms in Banach spaces

2002 ◽  
Vol 65 (2) ◽  
pp. 223-230 ◽  
Author(s):  
Marián Fabian ◽  
Vicente Montesinos ◽  
Václav Zizler
Keyword(s):  
Banach Spaces ◽  
Lower Semicontinuous ◽  
Compact Sets ◽  
Weakly Compact ◽  
Weakly Compact Sets

Two smoothness characterisations of weakly compact sets in Banach spaces are given. One that involves pointwise lower semicontinuous norms and one that involves projectional resolutions of identity.

FIXED POINT THEOREMS FOR GENERAL CLASSES OF MAPS ACTING ON TOPOLOGICAL VECTOR SPACES

2011 ◽  
Vol 04 (03) ◽  
pp. 373-387 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Mohamed-Aziz Taoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Vector Spaces ◽  
Compact Sets ◽  
Multivalued Maps ◽  
Weakly Compact ◽  
Topological Vector Spaces ◽  
Admissible Maps ◽  
Weakly Compact Sets ◽  
Locally Convex

We present new fixed point theorems for multivalued [Formula: see text]-admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray–Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

Sign in / Sign up

Export Citation Format

Share Document