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- W2377135416 abstract "Several characterizations of b-AM-compact operators are considered in this paper, we show that: 1) If F is an infinite-dimensional Banach lattice, then E is a KB-space if and only if every AM-compact operator from E into F is b-AM-compact. 2) The Banach lattice E is a discrete KB-space if and only if every continuous operator from E into Banach lattice F is b-AM-compact. 3) If the topological dual E is discrete, then every b-weakly compact operator from Banach E into Banach space X is b-AM-compact. Moreover, following prop- erties about the problems of domination in the class of positive b-AM-compact operators are established: 1) If E and F are two Banach lattices, then for all operators S, T : E → F such that 0 ≤ S ≤ T and T is b-AM-compact, the operator S is b-AM-compact if and only if the norm of F is order continuous or E is discrete. 2) If S, T are two operators from E into F with 0 ≤ S ≤ T, if T is b-AM-compact, then S2 is likewise b-AM-compact." @default.
- W2377135416 created "2016-06-24" @default.
- W2377135416 creator A5080633781 @default.
- W2377135416 date "2010-01-01" @default.
- W2377135416 modified "2023-09-27" @default.
- W2377135416 title "b-AM-compact Operators on Banach Lattices" @default.
- W2377135416 hasPublicationYear "2010" @default.
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