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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Commutants for some classes of Hausdorff matrices

Author: B. E. Rhoades
Journal: Proc. Amer. Math. Soc. 123 (1995), 2745-2755
MSC: Primary 40G05; Secondary 40C05
MathSciNet review: 1301525
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Abstract: Let $ \Gamma $ denote the algebra of all bounded infinite matrices on c, the space of convergent sequences, $ \Delta $ the subalgebra of $ \Gamma $ consisting of lower triangular matrices. It is well known that, if H is any Hausdorff matrix with distinct diagonal entries, then the commutant of H in $ \Delta $ contains only Hausdorff matrices. In previous work the author has shown that a necessary condition for the commutant of a Hausdorff matrix H to be the same in $ \Gamma $ and $ \Delta $ is that H have distinct diagonal entries, but that the condition is not sufficient. In this paper it is shown that certain Hausdorff matrices, with distinct diagonal entries, have the same commutants in $ \Gamma $ and $ \Delta $.

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PII: S 0002-9939(1995)1301525-5
Keywords: Cesàro, commutant, Euler, Hausdorff matrices, Hölder
Article copyright: © Copyright 1995 American Mathematical Society