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arXiv · 1312.7090

Non-self-adjoint resolutions of the identity and associated operators

A. Inoue·C. Trapani
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Abstract

Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $\{X(λ)\}_{λ\in {\mb R}}$, whose adjoints constitute also a resolution of the identity, are studied . In particular, it is shown that a closed operator $B$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $B=TAT^{-1}$ where $A$ is self-adjoint and $T$ is a bounded operator with bounded inverse.

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A. Inoue, C. Trapani. 2014-01-14. Non-self-adjoint resolutions of the identity and associated operators. https://arxiv.org/abs/1312.7090

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