Balanced Operators and Operator Domains

Konrad Schmüdgen

Balanced Operators and Operator Domains

Functional Analysis 2021-03-15 v2

Authors: Konrad Schmüdgen

Abstract

We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$ . Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed. A characterization of the domain equality $\cD(A)=\cD(B)$ for positive self-adjoint operators $A$ and $B$ with bounded inverses is given in terms of their spectral measures.

Keywords

operator theory on hilbert spaces operator theory numerical range

Cite

@article{arxiv.2102.09044,
  title  = {Balanced Operators and Operator Domains},
  author = {Konrad Schmüdgen},
  journal= {arXiv preprint arXiv:2102.09044},
  year   = {2021}
}

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The paper contains an error. I work on repairing, but I dont know whether or when this will be done. Please withdraw the paper

Balanced Operators and Operator Domains

Abstract

Keywords

Cite

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