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

Camillo Trapani, Atsushi Inoue

Research output: Contribution to journalArticlepeer-review

3 Citations (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.
Original languageEnglish
Pages (from-to)1531-1546
Number of pages16
JournalComplex Analysis and Operator Theory
Volume8
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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