Vol. 46, No. 1, 1973

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Some inclusion theorems for sequence spaces

Grahame Bennett

Vol. 46 (1973), No. 1, 17–30
Abstract

The purpose of this paper is to study inclusion theorems for some of the more familiar sequence spaces. Necessary and sufficient conditions are given for an FK-space to contain each of the spaces bv0, bv, lp,0 < p < , and c0. It is also shown that the Hardy space Hp,0 < p < 1, is a barrelled subspace of its containing Banach space Bp. This leads to new results concerning multipliers of Hp and to new estimates on the growth of the Taylor coefficients of Bp functions.

Mathematical Subject Classification 2000
Primary: 46A45
Milestones
Received: 4 February 1972
Published: 1 May 1973
Authors
Grahame Bennett