Search results for "Spectral theorem"

showing 2 items of 12 documents

Operators which have a closed quasi-nilpotent part

2002

We find several conditions for the quasi-nilpotent part of a bounded operator acting on a Banach space to be closed. Most of these conditions are established for semi-Fredholm operators or, more generally, for operators which admit a generalized Kato decomposition. For these operators the property of having a closed quasi-nilpotent part is related to the so-called single valued extension property.

Unbounded operatorDiscrete mathematicsPure mathematicsApproximation propertyApplied MathematicsGeneral MathematicsSpectrum (functional analysis)Finite-rank operatorSpectral theoremOperator theoryOperator normFourier integral operatorMathematicsProceedings of the American Mathematical Society
researchProduct

Refinements of PIP-Spaces

2009

We have seen in Section 1.5, that the compatibility relation underlying a pip-space may always be coarsened, but not refined in general. There is an exception, however, namely the case of a scale of Hilbert spaces and analogous structures. We shall describe it in this section.

Unbounded operatorPure mathematicssymbols.namesakeScale (ratio)Section (archaeology)Compatibility relationHilbert spacesymbolsSpectral theoremMathematics
researchProduct