Elementary Operators on Standard Operator Algebras

Authors: Molnár L.1; Scaronemrl P.2

Source: Linear and Multilinear Algebra, Volume 50, Number 4, 1 January 2002 , pp. 315-319(5)

Publisher: Taylor and Francis Ltd

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Abstract:

We present a new simple proof of the structural result for elementary operators on standard operator algebras. Using the idea of this short proof we can characterize surjective maps between standard operator algebras having a certain multiplicativity-like property appearing in the abstract definition of elementary operators of length one. In particular, we show that such maps are automatically additive.

Keywords: Standard operator algebra; Elementary operator

Document Type: Research article

Affiliations: 1: Institute of Mathematics and Informatics, University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary 2: Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

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