This article is cited in 17 papers

Research papers

The Wickstead Problem

A. E. Gutman^a, A. G. Kusraev^b, S. S. Kutateladze<sup>a

a</sup> Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Institute of Applied Mathematics and Informatics, Vladikavkaz, Russia

Abstract: In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice.

Keywords: Band preserving operator, universally complete vector lattice, $\sigma$-distributive Boolean algebra, local Hamel basis, transcendence basis, derivation, Boolean valued representation.

UDC: 517.98

MSC: 46A40, 47B60, 12F20, 03C90, 03C98

Received February 13, 2008, published July 1, 2008

Language: English

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