2019•TURKISH JOURNAL OF MATHEMATICSOpen access

The relation between b-weakly compact operator and KB-operator

Bahri Turan, Birol Altın

Abstract

Our aim is to solve the problem asked by Bahramnezhad and Azar in "KB-operators on Banach lattices and their relationships with Dunford-Pettis and order weakly compact operators". We show that a continuous operators R from a Banach lattice N into a Banach space M is a b-weakly compact operator if and only if R is a KB-operator.

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Key concepts: Mathematics, Compact operator, Finite-rank operator, Strictly singular operator, Approximation property, Operator (biology), Pseudo-monotone operator, Pure mathematics