On the operator equation α + α − 1 = β + β − 1

A. B. Thaheem

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-4

Abstract:

Let α , β be ∗ -automorphisms of a von Neumann algebra M satisfying the operator equation α + α − 1 = β + β − 1 . In this paper we use new techniques (which are useful in noncommutative situations as well) to provide alternate proofs of the results:- If α , β commute then there is a central projection p in M such that α = β on M P and α = β − 1 on M ( 1 − P ) ; If M = B ( H ) , the algebra of all bounded operators on a Hilbert space H , then α = β or α = β − 1 .

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:273941

DOI: 10.1155/S0161171286000923

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