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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 187536, 19 pages
http://dx.doi.org/10.1155/2013/187536
Research Article

Köthe-Bochner Spaces and Some Geometric Properties Related to Rotundity and Smoothness

Department of Mathematics, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany

Received 24 May 2013; Accepted 27 June 2013

Academic Editor: T. S. S. R. K. Rao

Copyright © 2013 Jan-David Hardtke. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In 2000, Kadets et al. introduced the notions of acs, luacs, and uacs spaces, which form common generalisations of well-known rotundity and smoothness properties of Banach spaces. In a recent paper, the author introduced some further related notions and investigated the behaviour of these geometric properties under the formation of absolute sums. The present paper is in a sense a continuation of this work. Here we will study the behaviour of the said properties under the formation of Köthe-Bochner spaces, thereby generalising some results of G. Sirotkin on the acs, luacs, and uacs properties of -Bochner spaces.