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 | References | Similar Articles | Additional Information

Abstract: Let denote the algebra of all bounded infinite matrices on *c*, the space of convergent sequences, the subalgebra of 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 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 and 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 and .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1301525-5

Keywords:
Cesàro,
commutant,
Euler,
Hausdorff matrices,
Hölder

Article copyright:
© Copyright 1995
American Mathematical Society