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http://dx.doi.org/10.4134/BKMS.b160037

BOUNDED AND UNBOUNDED OPERATORS SIMILAR TO THEIR ADJOINTS  

Dehimi, Souheyb (Department of Mathematics University of Oran 1)
Mortad, Mohammed Hichem (Department of Mathematics University of Oran 1)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 215-223 More about this Journal
Abstract
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 well known results by Sheth and Williams.
Keywords
similarity; bounded and unbounded operators; closed; self-adjoint; normal; hyponormal operators; unitary cramped operators; numerical range;
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