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

Camillo Trapani, Atsushi Inoue

Risultato della ricerca: Articlepeer review

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 originale English 1531-1546 16 Complex Analysis and Operator Theory 8 Published - 2014

## All Science Journal Classification (ASJC) codes

• Computational Mathematics
• Computational Theory and Mathematics
• Applied Mathematics