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Quaestiones Mathematicae 31(2008), 151161. c 2008 NISC Pty Ltd, www.nisc.co.za
 

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
COSINGULAR OPERATORS
George Androulakis
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA.
E-Mail giorgis@math.sc.edu
Kevin Beanland
Department of Mathematics, Virginia Commonwealth University, Richmond, VA 23220,
USA.
E-Mail kbeanland@vcu.edu
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
theory.
1. Introduction. The main results of this paper use descriptive set theory

  

Source: Androulakis, George - Department of Mathematics, University of South Carolina

 

Collections: Mathematics