6533b830fe1ef96bd1296871
RESEARCH PRODUCT
Non-self-adjoint resolutions of the identity and associated operators
Camillo TrapaniAtsushi Inouesubject
Discrete mathematicsPure mathematicsApplied MathematicsHilbert spaceInverseOperator theoryMathematics::Spectral TheoryNon-self-adjoint resolution of identityFunctional Analysis (math.FA)Mathematics - Functional AnalysisComputational Mathematicssymbols.namesakeIdentity (mathematics)Operator (computer programming)Computational Theory and MathematicsSettore MAT/05 - Analisi MatematicaBounded functionsymbolsFOS: MathematicsSimilarity of operatorsSelf-adjoint operatorMathematicsResolution (algebra)description
Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $$\{X(\lambda )\}_{\lambda \in {\mathbb R}}$$ , 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 $$B=\textit{TAT}^{-1}$$ where $$A$$ is self-adjoint and $$T$$ is a bounded inverse.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-12-26 |