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2009•Владикавказский математический журналRequires access

ON RIESZ SPACES WITH b-PROPERTY AND b-WEAKLY COMPACT OPERATORS

Şafak Alpay, Birol Altın

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Abstract

An operator T : E → X between a Banach lattice E and a Banach space X is called b-weakly compact if T (B) is relatively weakly compact for each b-bounded set B in E. We characterize b-weakly compact operators among o-weakly compact operators. We show summing operators are b-weakly compact and discuss relation between Dunford–Pettis and b-weakly compact operators. We give necessary conditions for b-weakly compact operators to be compact and give characterizations of KB-spaces in terms of b-weakly compact operators defined on them.

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An operator T : E → X between a Banach lattice E and a Banach space X is called b-weakly compact if T (B) is relatively weakly compact for each b-bounded set B in E. We characterize b-weakly compact operators among o-weakly compact operators. We show summing operators are b-weakly compact and discuss relation between Dunford–Pettis and b-weakly compact operators. We give necessary conditions for b-weakly compact operators to be compact and give characterizations of KB-spaces in terms of b-weakly compact operators defined on them.

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Available abstract

An operator T : E → X between a Banach lattice E and a Banach space X is called b-weakly compact if T (B) is relatively weakly compact for each b-bounded set B in E. We characterize b-weakly compact operators among o-weakly compact operators. We show summing operators are b-weakly compact and discuss relation between Dunford–Pettis and b-weakly compact operators. We give necessary conditions for b-weakly compact operators to be compact and give characterizations of KB-spaces in terms of b-weakly compact operators defined on them.

Key concepts: Compact operator on Hilbert space, Mathematics, Compact operator, Approximation property, Compact space, Nuclear operator, Pure mathematics, Locally compact space

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