Interchangeability of unbounded linear operators: General theory of transmutativity
Miroslav Sova (1982)
Časopis pro pěstování matematiky
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Displaying similar documents to “Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions”
Interchangeability of unbounded linear operators: General theory of transmutativity
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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.
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For a scalar λ, two operators T and S are said to λ-commute if TS = λST. In this note we explore the pervasiveness of the operators that λ-commute with a compact operator by characterizing the closure and the interior of the set of operators with this property.
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We are mainly concerned with the result of Kaplansky on the composition of two normal operators in the case in which at least one of the operators is unbounded.