The Dunford-Pettis property in C*-algebras
Cho-Ho Chu, Bruno Iochum (1990)
Studia Mathematica
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Displaying similar documents to “An alternative Dunford-Pettis Property”
The Dunford-Pettis property in C*-algebras
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In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.
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The alternative Dunford-Pettis Property in the predual of a von Neumann algebra
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Let A be a type II von Neumann algebra with predual A⁎. We prove that A⁎ does not have the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φₙ) converging weakly to φ in A⁎ with ||φₙ|| = ||φ|| = 1 for all n ∈ ℕ and a weakly null sequence (xₙ) in A such that φₙ(xₙ) ↛ 0. This answers a question posed in [7].
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We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).
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We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.