Bull. Korean Math. Soc. 2017; 54(1): 215-223
Online first article November 1, 2016 Printed January 31, 2017
https://doi.org/10.4134/BKMS.b160037
Copyright © The Korean Mathematical Society.
Souheyb Dehimi and Mohammed Hichem Mortad
Ahmed Ben Bella, B.P. 1524, ElMenouar, Ahmed Ben Bella, B.P. 1524, El Menouar
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
MSC numbers: Primary 47A62; Secondary 47A05, 47A12, 47B20, 47B25
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