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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Matrix maps of bounded sequences in a Banach space


Author: I. J. Maddox
Journal: Proc. Amer. Math. Soc. 63 (1977), 82-86
MSC: Primary 40J05
MathSciNet review: 0447877
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Abstract: Matrices of bounded linear operators are applied to bounded sequences in a Banach space. The main result is related to Knopp's core theorem for scalar sequences and matrices. From the main result, necessary and sufficient conditions are given for a matrix of operators to map bounded sequences into null sequences in a Banach space.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0447877-9
Keywords: Infinite matrices of bounded linear operators, bounded sequences in a Banach space, core theorem
Article copyright: © Copyright 1977 American Mathematical Society