Search results for " 47B37"

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Operators on Partial Inner Product Spaces: Towards a Spectral Analysis

2014

Given a LHS (Lattice of Hilbert spaces) $V_J$ and a symmetric operator $A$ in $V_J$, in the sense of partial inner product spaces, we define a generalized resolvent for $A$ and study the corresponding spectral properties. In particular, we examine, with help of the KLMN theorem, the question of generalized eigenvalues associated to points of the continuous (Hilbertian) spectrum. We give some examples, including so-called frame multipliers.

Partial inner product spacesPure mathematicsGeneral MathematicsFOS: Physical sciencesresolventLattice (discrete subgroup)01 natural sciencessymbols.namesakeInner product spaceSettore MAT/05 - Analisi MatematicaPIP-spaceframe multipliers}lattices of Hilbert spacesSpectral analysis0101 mathematicsEigenvalues and eigenvectorsMathematical PhysicsMathematicsResolventframe multipliers010102 general mathematicsSpectrum (functional analysis)Spectral propertiesHilbert spaceMathematical Physics (math-ph)010101 applied mathematicssymbolsspectral properties of symmetric operatorsSpectral theory46Cxx 47A10 47B37
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Rolewicz-type chaotic operators

2015

In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.

Pure mathematicsApplied MathematicsExistential quantificationChaoticCardinality of the continuumFunctional Analysis (math.FA)Mathematics - Functional AnalysisCorollary47A16 47B37 37B99Settore MAT/05 - Analisi MatematicaNorm (mathematics)chaotic operators hypercyclic operators lineable Rolewicz operatorFOS: MathematicsCountable setLinear combinationAnalysisMathematics
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