scholarly journals Geometric and topological properties of certain $w^{\ast}$ compact convex subsets of double duals of banach spaces, which arise from the study of invariant means

1986 ◽  
Vol 30 (1) ◽  
pp. 148-174 ◽  
Author(s):  
Edmond E. Granirer
Keyword(s):  
Banach Spaces ◽  
Compact Convex ◽  
Topological Properties ◽  
Invariant Means ◽  
Convex Subsets

Geometric and Topological Properties of Certain w* Compact Convex sets which Arise from the Study of Invariant Means

1985 ◽  
Vol 37 (1) ◽  
pp. 107-121 ◽  
Author(s):  
Edmond E. Granirer
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Fixed Points ◽  
Convex Sets ◽  
Compact Convex ◽  
Topological Properties ◽  
Bounded Linear ◽  
Invariant Means ◽  
Image Position ◽  
Set Of Points

Let E be a Banach space, A a subset of its dual E*.x0 ∊ A is said to be a w*Gδ point of A if there are xn ∊ E and scalars γn, n = 1,2, 3 … such thatDenote by w*Gδ{A} the set of all w*Gδ points of A. If S is a semigroup of maps on E* and K ⊂ E*, denote byi.e., the set of points x* in the w*closure of K which are fixed points of S (i.e., sx* = x* for each s in S}. An operator will mean a bounded linear map on a Banach space and Co B will denote the convex hull of B ⊂ E.

scholarly journals Strongly exposed points and a characterization of l1 (Γ) by the Schur property

1987 ◽  
Vol 30 (3) ◽  
pp. 397-400 ◽  
Author(s):  
Ioannis A. Polyrakis
Keyword(s):  
Banach Spaces ◽  
Banach Lattice ◽  
Positive Cone ◽  
Schur Property ◽  
Positive Elements ◽  
Strongly Exposed Points ◽  
Ordered Banach Spaces ◽  
Convex Subsets ◽  
Quasi Interior

In this paper we study the existence of strongly exposed points in unbounded closed and convex subsets of the positive cone of ordered Banach spaces and we prove the following characterization for the space l1(Γ): A Banach lattice X is order-isomorphic to l1(Γ) iff X has the Schur property and X* has quasi-interior positive elements.

scholarly journals Some geometric and topological properties of Banach spaces via ball coverings

2011 ◽  
Vol 377 (2) ◽  
pp. 874-880 ◽  
Author(s):  
Lixin Cheng ◽  
Bo Wang ◽  
Wen Zhang ◽  
Yu Zhou
Keyword(s):  
Banach Spaces ◽  
Topological Properties

scholarly journals Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Sudhir Kumar ◽  
Vijay Kumar ◽  
S. S. Bhatia
Keyword(s):  
Sequence Spaces ◽  
Modulus Function ◽  
Difference Sequence ◽  
Topological Properties ◽  
Ideal Convergence ◽  
Difference Sequences ◽  
Invariant Means ◽  
Difference Sequence Spaces

The main objective of this paper is to introduce a new kind of sequence spaces by combining the concepts of modulus function, invariant means, difference sequences, and ideal convergence. We also examine some topological properties of the resulting sequence spaces. Further, we introduce a new concept of SθσΔm(I)-convergence and obtain a condition under which this convergence coincides with above-mentioned sequence spaces.

scholarly journals Twisted properties of banach spaces

2001 ◽  
Vol 89 (2) ◽  
pp. 217 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Manuel Gonzáles ◽  
Anatolij M. Plichko ◽  
David Yost
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Topological Properties ◽  
Space Property ◽  
Compactly Generated

If $\mathcal P$, $\mathcal Q$ are two linear topological properties, say that a Banach space $X$ has the property $\mathcal P$-by-$\mathcal Q$ (or is a $\mathcal P$-by-$\mathcal Q$ space) if $X$ has a subspace $Y$ with property $\mathcal P$ such that the corresponding quotient $X/Y$ has property $\mathcal Q$. The choices $\mathcal P,\mathcal Q \in\{\hbox{separable, reflexive}\}$ lead naturally to some new results and new proofs of old results concerning weakly compactly generated Banach spaces. For example, every extension of a subspace of $L_1(0,1)$ by a WCG space is WCG. They also give a simple new example of a Banach space property which is not a 3-space property but whose dual is a 3-space property.

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