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arXiv · 1409.3016

Operators on Partial Inner Product Spaces: Towards a Spectral Analysis

Jean-Pierre Antoine·Camillo Trapani
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Abstract

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.

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Jean-Pierre Antoine, Camillo Trapani. 2014-09-10. Operators on Partial Inner Product Spaces: Towards a Spectral Analysis. https://doi.org/10.1007/s00009-014-0499-6

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