Related papers: Weak Topologies

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the…

We completely characterize the weak differentiability (or, in other words Gateaux differentiability) of the norm in the spaces of bounded multilinear maps. Also, we obtain a multilinear generalization of the well-known Bhatia-\v{S}emrl…

This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability.

This paper deals with the notion of weak Lawvere-Tierney topology on a topos. Our motivation to study such a notion is based on the observation that the composition of two Lawvere-Tierney topologies is no longer idempotent, when seen as a…

We inspect the properties of reflexive Banach algebras that are related to the pointwise products of its weakly null sequences.

Local indices at isolated fixed points of a differentiable compact nonlinear map $T$ on Banach spaces will be discussed. These results are applied to establish the existence of nontrivial solutions. As an example, the existence of…

In this paper, we introduce the concept of weak fuzzy linear topology on a fuzzy topological vector space as a generalization of usual weak topology. We prove that this topology consists of all weakly lower semi-continuous fuzzy sets on a…

Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…

Let $B$ be a Banach $A-bimodule$. We introduce the weak topological centers of left module action and we show it by $\tilde{{Z}}^\ell_{B^{**}}(A^{**})$. For a compact group, we show that $L^1(G)=\tilde{Z}_{M(G)^{**}}^\ell(L^1(G)^{**})$ and…

In this paper, we study nonlinear embeddings between Banach spaces. More specifically, the goal of this paper is to study weaker versions of coarse and uniform embeddability, and to provide suggestive evidences that those weaker embeddings…

In this paper, we study on weak $I^K$-Cauchy condition as a generalization of weak $I^*$-Cauchy condition in a normed space. We investigate the relationship between weak $I$-Cauchy and weak $I^K$-Cauchy sequences using $AP(I,K)$-condition.…

In this note we study the weak topology on paired modules over a (not necessarily commutative) ground ring. Over QF rings we are able to recover most of the well known properties of this topology in the case of commutative base fields. The…

In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover,…

We prove that if a unital Banach algebra $A$ is the dual of a Banach space $\pd{A}$, then the set of weak* continuous states is weak* dense in the set of all states on $A$. Further, weak* continuous states linearly span $\pd{A}$.

In this paper we give a various conditions for which the tuple $\mathcal{T} = (T_{1} , T_{2} , ... , T_{n})$ of commutative bounded linear operators on an infinite dimensional ( real , complex ) Banach space X is orbit reflexive. After we…

Weak topologies that yield weak convergence for bounded sequences and nets in CAT($0$) spaces have been studied in the past. We are here concerned with weak topologies that yield weak convergence of unbounded sequences and nets. We analyze…

In the Trotter-Kato approximation theorem for C_0-semigroups on Banach spaces, we replace the strong by the weak operator topology and discuss the validity of the relevant implications.

A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly…

A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is…

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…