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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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