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J. Math. Anal. Appl. 333 (2007) 12541263 www.elsevier.com/locate/jmaa
 

Summary: J. Math. Anal. Appl. 333 (2007) 12541263
www.elsevier.com/locate/jmaa
A new method for constructing invariant subspaces
George Androulakis
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
Received 17 July 2006
Available online 16 December 2006
Submitted by J. Diestel
Abstract
The new idea that is used in this article for producing non-trivial (closed) invariant subspaces of (bounded
linear) operators on reflexive Banach spaces, is the use of fixed points of set-valued functions. The advantage
of this new method is that it is reasonable to expect that the famous method of Lomonosov for producing
invariant subspaces using fixed points of functions, can be viewed as a special case of the use of fixed points
of set-valued functions. Further uses of this new idea and open questions are suggested at the end of the
article.
2006 Elsevier Inc. All rights reserved.
Keywords: Invariant subspaces; Fixed points of set-valued functions
1. Introduction
Let X be a Banach space (always of dimension larger than 1) and T L(X) (i.e. T :X X
is a (bounded linear) operator). A (closed) subspace Y of X is called an invariant subspace of T

  

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

 

Collections: Mathematics