Bulletin of the Korean Mathematical Society (대한수학회보)

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BOUNDED AND UNBOUNDED OPERATORS SIMILAR TO THEIR ADJOINTS

  • Received : 2016.01.15
  • Published : 2017.01.31
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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.

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References

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