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The space lip $ \alpha $ and certain other spaces have duals with Cesàro bases


Author: Martin Buntinas
Journal: Proc. Amer. Math. Soc. 57 (1976), 233-237
MSC: Primary 46A45
DOI: https://doi.org/10.1090/S0002-9939-1976-0477673-7
MathSciNet review: 0477673
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Abstract: Banach sequence spaces whose duals are Banach sequence spaces with Toeplitz bases are characterized. For example, the duals of the lip $ \alpha $ spaces, for $ 0 < \alpha < 1$, are shown to have Cesàro bases. Also reflexive spaces with a Toeplitz basis are characterized and an equivalent form of the well-known theorem of F. and M. Riesz on the absolute continuity of measures is given.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0477673-7
Article copyright: © Copyright 1976 American Mathematical Society

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