Unconditional convergence and invertibility of multipliers

Abstract

In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for unconditional convergence and invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples which show that the given assertions cover different classes of multipliers are given. If a multiplier is invertible, a formula for the inverse operator is determined. The case when one of the sequences is a Riesz basis is completely characterized.

31 pages; changes to previous version: 1.) the results from the previous version are extended to the case of complex symbols m. 2.) new statements about the unconditional convergence and boundedness are added (3.1,3.2 and 3.3). 3.) the proof of a preliminary result (Prop. 2.2) was moved to a conference proceedings [29]. 4.) Theorem 4.10. became more detailed

References in corpus (2)

• Multipliers for p-Bessel sequences in Banach spaces
• Detailed characterization of unconditional convergence and invertibility of multipliers

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