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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.
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참고문헌 (15)
참고문헌 신청
A. Grothendieck / 1955 / Produits tensoriels topologiques et espaces nucl´eaires / Mem. Amer. Math. Soc 16 : 140 ~
A. Lima / 2000 / Isometric factorization of weakly compact operators and the approximation property / Israel J. Math 119 : 325 ~ 348
C. Choi / 2011 / Hahn-Banach theorem for the compact convergence topology and applications to approximation properties / Houston J. Math 37 : 1157 ~ 1164
G. Godefroy / 1988 / Duality in spaces of operators and smooth norms on Banach spaces, Illinois / J. Math 32 (4) : 672 ~ 695
J. Lindenstrauss / 1977 / Classical Banach Spaces / Springer
A. Lima / 2000 / Isometric factorization of weakly compact operators and the approximation property / Israel J. Math 119 : 325 ~ 348
C. Choi / 2011 / Hahn-Banach theorem for the compact convergence topology and applications to approximation properties / Houston J. Math 37 : 1157 ~ 1164
G. Godefroy / 1988 / Duality in spaces of operators and smooth norms on Banach spaces, Illinois / J. Math 32 (4) : 672 ~ 695
J. Lindenstrauss / 1977 / Classical Banach Spaces / Springer
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