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ON RANK TWO LINEAR TRANSFORMATIONS AND REFLEXIVITY

By Edward A. Azoff and Marek Ptak

Abstract

Abstract. We study operator algebras generated by commuting families of nilpotents. In order for such an algebra A to be re°exive, it is necessary that each ideal generated by a rank two member of A be one{dimensional. When the underlying space is a ¯nite{dimensional Hilbert space and the nilpotents in question doubly commute in the sense that they commute with each other's adjoints, the condition is also su±cient. Doubly commuting families of nilpotents admit simultaneous Jordan Canonical Forms and re°exivity of A can also be characterized in terms of Jordan block sizes. In particular, our results generalize work of J. Deddens and P. Fillmore on singly{ generated operator algebras. 1. Introduction. Mos

Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.512
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