Weak∗ closures and derived sets in dual Banach spaces
نویسندگان
چکیده
The main results of the paper: (1) The dual Banach space X∗ contains a linear subspace A ⊂ X∗ such that the set A of all limits of weak∗ convergent bounded nets in A is a proper norm-dense subset of X∗ if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subset A ⊂ X∗ such that A 6= A ∗ (the latter denotes the weak∗ closure of A). (3) Let X be a quasi-reflexive Banach space and A ⊂ X∗ be an absolutely convex subset. Then A = A ∗ .
منابع مشابه
Envelopes of Open Sets and Extending Holomorphic Functions on Dual Banach Spaces
We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.
متن کاملDerivations on dual triangular Banach algebras
Ideal Connes-amenability of dual Banach algebras was investigated in [17] by A. Minapoor, A. Bodaghi and D. Ebrahimi Bagha. They studied weak∗continuous derivations from dual Banach algebras into their weak∗-closed two- sided ideals. This work considers weak∗-continuous derivations of dual triangular Banach algebras into their weak∗-closed two- sided ideals . We investigate when weak∗continuous...
متن کاملWeak and $(-1)$-weak amenability of second dual of Banach algebras
For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things, we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.
متن کاملModule Amenability of module dual Banach algebras
In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...
متن کاملWeak amenability of (2N)-th dual of a Banach algebra
In this paper by using some conditions, we show that the weak amenability of (2n)-th dual of a Banach algebra A for some $ngeq 1$ implies the weak amenability of A.
متن کامل