The space lip 𝛼 and certain other spaces have duals with Cesàro bases

Buntinas, Martin

doi:10.1090/S0002-9939-1976-0477673-7

The space lip $\alpha$ and certain other spaces have duals with Cesàro bases
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Proc. Amer. Math. Soc. 57 (1976), 233-237 Request permission

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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