Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1973-0320796-5
MathSciNet review: 0320796
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47B10

Retrieve articles in all journals with MSC: 47B10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0320796-5
Keywords: Dominated operator, absolutely summing operator, vector measure of bounded variation
Article copyright: © Copyright 1973 American Mathematical Society