BOUNDED AND UNBOUNDED OPERATORS SIMILAR TO THEIR ADJOINTS
Copyright policy )BOUNDED AND UNBOUNDED OPERATORS SIMILAR TO THEIR ADJOINTS
In this paper, we establish results about operators similar to their adjoints. This is carried out in the setting of bounded and also unbounded operators on a Hilbert space. Among the results, we prove that an unbounded closed operator similar to its adjoint, via a cramped unitary operator, is self-adjoint. The proof of this result works also as a new proof of the celebrated result by Berberian on the same problem in the bounded case. Other results on similarity of hyponormal unbounded operators and their self-adjointness are also given, generalizing famous results by Sheth and Williams.
08 pages
Mathematics - Functional Analysis, Primary 47A62, Secondary 47A05, 47A12, 47B20, 47B25, Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA), Functional Analysis (math.FA)
Mathematics - Functional Analysis, Primary 47A62, Secondary 47A05, 47A12, 47B20, 47B25, Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA), Functional Analysis (math.FA)
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