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Transactions of the American Mathematical Society

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Absolutely summing and dominated operators on spaces of vector-valued continuous functions

Author: Charles Swartz
Journal: Trans. Amer. Math. Soc. 179 (1973), 123-131
MSC: Primary 47B10
MathSciNet review: 0320796
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Abstract: A. Pietsch has shown that the class of dominated linear operators on $ C(S)$ coincides with the class of absolutely summing operators. If the space $ C(S)$ is replaced by $ {C_X}(S)$, where X is a Banach space, this is no longer the case. However, any absolutely summing operator is always dominated, and the classes of operators coincide exactly when X is finite dimensional. A characterization of absolutely summing operators on $ {C_X}(S)$ is given.

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Keywords: Dominated operator, absolutely summing operator, vector measure of bounded variation
Article copyright: © Copyright 1973 American Mathematical Society