2014/05/30 by Dehimi, Souheyb, Mortad, Mohammed Hichem
#47A12 #47B20 #47B25 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47A62 #Secondary 47A05
paper · doi:10.48550/arxiv.1405.7941
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.