Work

The Lifting Property for Frame Multipliers and Toeplitz Operators

Year: 2026

Type: article

Abstract: Frame multipliers are an abstract version of Toeplitz operators in frame theory and consist of a composition of a multiplication operator with the analysis and synthesis operators. Whereas the boundedness properties of frame multipliers on Banach spaces associated to a frame, so-called coorbit spaces, are well understood, their invertibility is much more difficult. We show that frame multipliers with a positive symbol are Banach space isomorphisms between the corresponding coorbit spaces. The results resemble the lifting theorems in the theory of Besov spaces and modulation spaces. Indeed, the application of the abstract lifting theorem to Gabor frames yields a new lifting theorem between modulation spaces. A second application to Fock spaces yields isomorphisms between weighted Fock spaces. The main techniques are taken from the theory of localized frames and the spectral invariance of matrix algebras.

Source: Integral Equations and Operator Theory

DOI: 10.1007/s00020-026-02868-4

Authors: Peter Balazs, Karlheinz Gröchenig

Institutions: Austrian Academy of Sciences, Acoustics Research Institute, Interdisciplinary Transformation University Austria, University of Vienna

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Universität Wien