A generalization of b-weakly compact operators

2019/05/25 by Azar, Kazem Haghnejad
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.10543

Abstract

A. Bahramnezhad and K. Haghnejad Azar introduced the classes of KB-operators and WKB-operators, and they studied some of theirs properties. In the present paper, we give answer for an open problem from that paper, which two classifications of operators, b-weakly compact operators and KB-operators are different. A continuous operator T from a normed vectoe lattice E into a normed space X is said to be KB-operator (respectively, WKB-operator) if \Tx_n\_n has a norm (respectively, weak) convergent subsequence in X for every positive increasing sequence \x_n\_n in the closed unit ball B_E of E. We investigate some other properties of KB-operators and its relationships with b-weakly compact operators.

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