Weakly compact operators from a B-space into the space of Bochner integrable functions
Charles Swartz (1973)
Colloquium Mathematicae
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Charles Swartz (1973)
Colloquium Mathematicae
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A.K. Snyder, Matthew Schaffer (1986)
Mathematische Zeitschrift
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J. H'Michane, A. El Kaddouri, K. Bouras, M. Moussa (2013)
Commentationes Mathematicae Universitatis Carolinae
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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).
Milan Konečný (1999)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Jesús M. Fernández Castillo (1990)
Extracta Mathematicae
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A sequence (x) in a Banach space X is said to be weakly-p-summable, 1 ≤ p < ∞, when for each x* ∈ X*, (x*x) ∈ l. We shall say that a sequence (x) is weakly-p-convergent if for some x ∈ X, (x - x) is weakly-p-summable.
Jesús M. Martínez Castillo (1995)
Extracta Mathematicae
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Ioana Ghenciu (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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Suppose X and Y are Banach spaces, K is a compact Hausdorff space, Σ is the σ-algebra of Borel subsets of K, C(K,X) is the Banach space of all continuous X-valued functions (with the supremum norm), and T:C(K,X) → Y is a strongly bounded operator with representing measure m:Σ → L(X,Y). We show that if T is a strongly bounded operator and T̂:B(K,X) → Y is its extension, then T is limited if and only if its extension T̂ is limited, and that T* is completely continuous...
N. Ergun, T. Noiri (1990)
Matematički Vesnik
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Belmesnaoui Aqzzouz, Aziz Elbour, Mohammed Moussa (2012)
Mathematica Bohemica
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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.