The main purpose of this paper is to investigate the behavior of the Hilbert space valued functions ϕ that are obtained by applying a linear operator W to a resolution of the identity (i.e. a continuous Parseval frame) ζ. After reviewing the case when W is bounded with bounded inverse, we study, in more detail, generalized Riesz maps, i.e. the image of a ζ by an invertible closed linear operator W.
Antoine, J., Bellomonte, G., Trapani, C. (2025). Modifying a resolution of the identity by the action of a linear operator. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS [10.1142/S021988782540047X].
Modifying a resolution of the identity by the action of a linear operator
Jean-Pierre Antoine
;Giorgia Bellomonte;Camillo Trapani
2025-06-03
Abstract
The main purpose of this paper is to investigate the behavior of the Hilbert space valued functions ϕ that are obtained by applying a linear operator W to a resolution of the identity (i.e. a continuous Parseval frame) ζ. After reviewing the case when W is bounded with bounded inverse, we study, in more detail, generalized Riesz maps, i.e. the image of a ζ by an invertible closed linear operator W.
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