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By Edward A. Azoff and Marek Ptak


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
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