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The Hahn sequence space. III. (English) Zbl 1186.46020

Summary: The purpose of this article is to introduce a new class of sequence spaces, namely, semi-Hahn spaces. It is shown that the intersection of all semi-Hahn spaces is the Hahn space. There are already semi-conservative and semi-replete spaces in literature. However, there is no relation among these spaces. Some properties of the Hahn space which are not included in the first two parts [K.Chandrasekhara Rao, Bull.Calcutta Math.Soc.82, No.1, 72–78 (1990; Zbl 0719.46003); K.Chandrasekhara Rao and T.G.Srinivasalu, Y.Y.U.J.Fac.Edu.1, No.2, 43–45 (1996; per bibl.)] are given, before introducing semi-Hahn spaces. In fact, conditions for inclusion of the Hahn space \(h\) in an \(FK\)-space, AB-property of \(h\), and inclusion of the distinguished subspace \(B^+(h)\) are studied.

MSC:

46B45 Banach sequence spaces

Citations:

Zbl 0719.46003
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