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Operators not positive with respect to any basis

 

作者: Angela Spalsbury,  

 

期刊: Quaestiones Mathematicae  （Taylor Available online 2000）
卷期: Volume 23, issue 4  

页码: 489-494

 

ISSN:1607-3606

 

年代: 2000

 

DOI:10.2989/16073600009485991

 

出版商: Taylor & Francis Group

 

关键词: INVARIANT SUBSPACES;POSITIVE OPERATORS

 

数据来源: Taylor

 

摘要:

In this paper we use an equivalent form of Titchmarsh's Convolution theorem to show that the Volterra operator is an example of a quasi-nilpotent operator on a Hilbert space that is not positive with respect to any basis ofL2(0,1). In proving this, it then becomes clear how to generalize this to any operatorTwith the property that ifMis an invariant subspace ofTandTx∈Mthenx∈M.

 

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