Summary: Quaestiones Mathematicae 31(2008), 151161.
c 2008 NISC Pty Ltd, www.nisc.co.za
DESCRIPTIVE SET THEORETIC METHODS
APPLIED TO STRICTLY SINGULAR AND STRICTLY
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.
Department of Mathematics, Virginia Commonwealth University, Richmond, VA 23220,
Abstract. The class of strictly singular operators originating from the dual of a
separable Banach space is written as an increasing union of 1 subclasses which are
defined using the Schreier sets. A question of J. Diestel, of whether a similar result
can be stated for strictly cosingular operators, is studied.
Mathematics Subject Classification (2000): 47B07, 47A15.
Key words: Strictly singular and cosingular operators, Schreier families, descriptive set
1. Introduction. The main results of this paper use descriptive set theory