This is an announcement for the paper "On the relationship between order bounded operators, topologically bounded operators and topologically continuous operators" by Liang Hong.
Abstract: The relationship between order bounded operators and order continuous operators has been investigated by several authors. The purpose of this paper is to study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. We give conditions for (i) the space of topologically continuous operators to be an ideal of the space of order bounded operators; this result generalizes the Nakano-Roberts Theorem; (ii) the space of topologically continuous operators to be a band of the space of order bounded operators; (iii) the space of order bounded operators to coincide with the space of topologically bounded operators; (iv) the space of order bounded operators to coincide with the space of topologically continuous operators. In addition, a set of counterexamples are given for illustration purpose; these counterexamples are interesting in their own rights and contribute to the literature.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B60, 47B65, Secondary 46A40, 06B30, 06F30
Submitted from: hong@rmu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.08016
or