Inclusions between FK spaces and Kuttner's theorem

Author:

Maddox I. J.

Abstract

The result known as Kuttner's theorem [2] asserts that if 0 < p < 1 and A is a Toeplitz matrix then there is a sequence which is strongly Cesàro summable with index p but which is not A summable. This theorem was extended by Maddox[3] to coregular matrices, and Thorpe [9] gave a further extension by showing that if 0 < p < 1 and X is a locally convex FK space with Xw0(p) then Xl. Here, w0(p) denotes the space of sequences strongly summable to 0, i.e. xw0(p) if and only ifand l denotes the space of bounded sequences. Other proofs of Thorpe's extension and related results appear in Maddox[4, 5].

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference10 articles.

1. Sequence spaces defined by a modulus

2. Note on strong summability;Kuttner;J. London Math. Soc,1946

3. Inclusion theorems and semiconservative FK spaces

4. On Kuttner's Theorem

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