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arXiv · 2102.09044

Balanced Operators and Operator Domains

Konrad Schmüdgen
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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.

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Konrad Schmüdgen. 2021-02-17. Balanced Operators and Operator Domains. https://arxiv.org/abs/2102.09044

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