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Proceedings of the American Mathematical Society

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

 

 

$ S$-limits and $ A$-summability


Author: Howard T. Bell
Journal: Proc. Amer. Math. Soc. 61 (1976), 49-53
MSC: Primary 40C05
DOI: https://doi.org/10.1090/S0002-9939-1976-0427890-7
MathSciNet review: 0427890
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Abstract: Certain classes of subspaces of $ m$ are examined that are the domains of uniqueness of certain Banach type limits. These subspaces are identified as the bounded convergence domains of $ \mathcal{A}$-summability. As a corollary it is shown that the closure of $ bs$ in $ m$ is $ {f_0}$. Also we characterize those matrices whose convergence domains include these spaces in a manner analogous to Lorentz' characterization of strongly regular matrices.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0427890-7
Article copyright: © Copyright 1976 American Mathematical Society