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Inclusion Theorems for FX-Spaces

Published online by Cambridge University Press:  20 November 2018

Johann Boos
Johann Boos*
Affiliation:
Fernuniversität-Gesamthochschule, Hagen, Federal Republic of Germany
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The main result of this paper is Theorem 1 (in connection with Corollary 1 (e)), which says that the implication

*

holds for every separable FK-space F, for every FK-space E containing φ and for certain (for example, solid) FK-AB-spaces Y. At this, φ denotes the space of all finite sequences and WE is the set of all elements of E being weakly sectionally convergent.

This result was proved by Bennett and Kalton ([1] and [3]) in the special case that E contains all null sequences and that Y is the space m of all bounded sequences or the space of all sequences almost converging to zero.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 3 , 01 June 1987 , pp. 631 - 645
Copyright
Copyright © Canadian Mathematical Society 1987

References

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