Absolutely summing and dominated operators on spaces of vector-valued continuous functions
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- by Charles Swartz PDF
- Trans. Amer. Math. Soc. 179 (1973), 123-131 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 179 (1973), 123-131
- MSC: Primary 47B10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0320796-5
- MathSciNet review: 0320796