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Generalized b-weakly compact operators and their factorization through KR-spaces

Nabil Machrafi, Birol Altin

Abstract

We investigate more closely the class of generalized b-weakly compact operators on locally convex-solid Riesz spaces and we provide new sequential and operator characterizations in relation with the subject. We introduce explicitly the so-called KR-spaces in order to study the factorization problem for generalized b-weakly compact operators by analogy with the well-known factorization of b-weakly compact operators through KB-spaces.

Generalized b-weakly compact operators and their factorization through KR-spaces

Abstract

We investigate more closely the class of generalized b-weakly compact operators on locally convex-solid Riesz spaces and we provide new sequential and operator characterizations in relation with the subject. We introduce explicitly the so-called KR-spaces in order to study the factorization problem for generalized b-weakly compact operators by analogy with the well-known factorization of b-weakly compact operators through KB-spaces.
Paper Structure (5 sections, 28 theorems, 19 equations)

This paper contains 5 sections, 28 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Examples and some results
  3. Characterizations of gbwc operators
  4. KR-spaces
  5. Factorization of gbwc operators through KR-spaces

Key Result

Theorem 2.3

Let $\left( E,\tau \right)$ be a Dedekind-complete locally convex-solid Riesz space such that both the topologies $\tau$ and $\beta \left( E^{\prime },E\right)$ are Lebesgue. Then, each continuous gbwc operator $T$ from $E$ into a Banach space $X$ is weakly compact.

Theorems & Definitions (56)

  • Example 2.1
  • Example 2.2
  • Theorem 2.3
  • proof
  • Remark 2.4
  • Corollary 2.5
  • Example 2.6
  • Proposition 2.7
  • proof
  • Corollary 2.8
  • ...and 46 more