Given a Lattice of Hilbert spaces VJ and a symmetric operator A in VJ , 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.
Antoine, J., Trapani, C. (2016). Operators on Partial Inner Product Spaces: Towards a Spectral Analysis. MEDITERRANEAN JOURNAL OF MATHEMATICS, 13(1), 323-351 [10.1007/s00009-014-0499-6].
Operators on Partial Inner Product Spaces: Towards a Spectral Analysis
TRAPANI, Camillo
2016-01-01
Abstract
Given a Lattice of Hilbert spaces VJ and a symmetric operator A in VJ , 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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