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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 ${B}^{+}\left(h\right)$ are studied.
##### MSC:
 46B45 Banach sequence spaces