Search results for " 47A15"

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THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS

2018

We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.

Cauchy dual operatorsubnormal operatorPure mathematics[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]01 natural sciencessymbols.namesakeFOS: Mathematics0101 mathematicsconcave operatorMathematics47A05 47A15 47A20 47A63Mathematics::Functional AnalysisMathematics::Operator AlgebrasApplied Mathematics010102 general mathematicsHilbert spaceCauchy distributionExtension (predicate logic)Special class2-isometric liftingsA-contractionFunctional Analysis (math.FA)Dual (category theory)Mathematics - Functional Analysis010101 applied mathematicssymbolsAnalysis
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Notes on the subspace perturbation problem for off-diagonal perturbations

2014

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear; arXiv:1310.4360 (2013)] is adapted. It is shown that, in contrast to the case of general perturbations, the corresponding optimization problem can not be reduced to a finite-dimensional problem. A suitable choice of the involved parameters provides an upper bound for the solution of the optimization problem. In particular, this yields a rotation bound on the subspaces that is stronger than the previously known one from [J. Reine Angew. Math. (2013), DOI:10.1515/cre…

Pure mathematicsOptimization problemApplied MathematicsGeneral MathematicsDiagonalPerturbation (astronomy)Upper and lower boundsLinear subspaceFunctional Analysis (math.FA)Mathematics - Spectral TheoryMathematics - Functional AnalysisBounded functionFOS: Mathematics47A55 (Primary) 47A15 47B15 (Secondary)Spectral Theory (math.SP)Subspace topologyMathematics
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