Commutants for some classes of Hausdorff matrices
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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 $\Delta$.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2745-2755
- MSC: Primary 40G05; Secondary 40C05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1301525-5
- MathSciNet review: 1301525