On spaces of weak* to weak continuous compact operators
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This paper is concerned with the space Kw * (X*, Y ) of weak* to weak continuous compact operators from the dual space X* of a Banach space X to a Banach space Y . We show that if X* or Y* has the Radon-Nikod´ym property, C is a convex subset of Kw* (X*, Y ) with 0 ∈C and T is a bounded linear operator from X* into Y , then T ∈ C τc if and only if [수식] , where τc is the topology of uniform convergence on each compact subset of X, moreover, if T 2 Kw* (X*, Y ), here C need not to contain 0, then T ∈ Cτc if and only if T ∈ C in the topology of the operator norm. Some properties of Kw* (X* , Y ) are presented.
Abstract
This paper is concerned with the space Kw * (X*, Y ) of weak* to weak continuous compact operators from the dual space X* of a Banach space X to a Banach space Y . We show that if X* or Y* has the Radon-Nikod´ym property, C is a convex subset of Kw* (X*, Y ) with 0 ∈C and T is a bounded linear operator from X* into Y , then T ∈ C τc if and only if [수식] , where τc is the topology of uniform convergence on each compact subset of X, moreover, if T 2 Kw* (X*, Y ), here C need not to contain 0, then T ∈ Cτc if and only if T ∈ C in the topology of the operator norm. Some properties of Kw* (X* , Y ) are presented.
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