Non-Self-Adjoint Resolutions of the Identity and Associated Operators

Camillo Trapani, Atsushi Inoue

Risultato della ricerca: Article

3 Citazioni (Scopus)

Abstract

Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $\{X(\lambda)\}_{\lambda\in {\mb R}}$, 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.
Lingua originaleEnglish
pagine (da-a)1531-1546
Numero di pagine16
RivistaComplex Analysis and Operator Theory
Volume8
Stato di pubblicazionePublished - 2014

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All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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