Remarks on the structure of <i>C</i>-normal operators
Cun Wang, Jiayin Zhao, Sen Zhu
Abstract
We study a new class NC of Hilbert space operators, named C-normal operators for C a conjugation on a complex Hilbert space H, which were introduced by M. Ptak, K. Simik and A. Wicher. We provide a refined polar decomposition of C-normal operators. It is proved that those invertible ones are norm dense in NC and each contraction in NC is a mean of two unitary ones. For a dense class of operators, we prove that their C-normality coincides with C-symmetry. Also some illustrating examples are provided to show that NC is not closed under several natural operations.
Topics & Concepts
MathematicsInvertible matrixHilbert spacePolar decompositionNormalityUnitary operatorPure mathematicsUnitary stateOperator theoryCompact operator on Hilbert spaceNorm (philosophy)Operator normNuclear operatorClass (philosophy)Operator (biology)PolarCompact operatorApproximation propertyBanach spaceComputer sciencePhysicsGeneLawBiochemistryChemistryAstronomyPolitical scienceTranscription factorRepressorExtension (predicate logic)Artificial intelligenceProgramming languageStatisticsHolomorphic and Operator TheoryMatrix Theory and AlgorithmsAdvanced Topics in Algebra