منابع مشابه
Some properties of b-weakly compact operators on Banach lattices
In this paper we give some necessary and sufficient conditions for which each Banach lattice is space and we study some properties of b-weakly compact operators from a Banach lattice into a Banach space . We show that every weakly compact operator from a Banach lattice into a Banach space is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...
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Let X and Y be separable Banach spaces. Suppose Y either has a shrinking basis or Y is isomorphic to C(2N) andA is a subset of weakly compact operators from X to Y which is analytic in the strong operator topology. We prove that there is a reflexive space with a basis Z such that every T ∈ A factors through Z. Likewise, we prove that if A ⊂ L(X,C(2N)) is a set of operators whose adjoints have s...
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It is shown that the weakly closed algebra generated by a weakly compact group of operators on a Banach space is reflexive and equals its second commutant. Also, an example is given to show that the generator of a monothetic weakly compact group of operators need not have a logarithm in the algebra of all bounded linear operators on the underlying space. Let X be a complex Banach space, B(X) th...
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For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E/E) is defined by R(S)(x + E) = Sx + E (x ∈ E). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W (E) (here W (E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non–zero compact...
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Let V,W∞, andW be operator ideals of completely continuous, weakly ∞-compact, and weakly compact operators, respectively. We prove that V =W∞ ◦W−1. As an immediate application, the recent result by Dowling, Freeman, Lennard, Odell, Randrianantoanina, and Turett follows: the weak Grothendieck compactness principle holds only in Schur spaces.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 1999
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(99)80025-1