6533b7cefe1ef96bd1257abe

RESEARCH PRODUCT

Operators on Partial Inner Product Spaces: Towards a Spectral Analysis

Jean-pierre AntoineCamillo Trapani

subject

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

description

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.

yearjournalcountryeditionlanguage
2014-09-10
10.1007/s00009-014-0499-6http://arxiv.org/abs/1409.3016