Banach Journal of Mathematical Analysis

Bessel multipliers in Hilbert $C^\ast$--modules

Amir Khosravi and Morteza Mirzaee Azandaryani

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Abstract

In this paper we introduce Bessel multipliers, g-Bessel multipliers and Bessel fusion multipliers in Hilbert $C^\ast$--modules and we show that they share many useful properties with their corresponding notions in Hilbert and Banach spaces. We show that various properties of multipliers are closely related to their symbols and Bessel sequences, especially we consider multipliers when their Bessel sequences are modular Riesz bases and we see that in this case multipliers can be composed and inverted. We also study bounded below multipliers and generalize some of the results obtained for fusion frames in Hilbert spaces to Hilbert $C^\ast$--modules.

Article information

Source
Banach J. Math. Anal., Volume 9, Number 3 (2015), 153-163.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419001709

Digital Object Identifier
doi:10.15352/bjma/09-3-11

Mathematical Reviews number (MathSciNet)
MR3296131

Zentralblatt MATH identifier
1311.42083

Subjects
Primary: 42C15: General harmonic expansions, frames
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

Keywords
Hilbert $C^\ast$--module Bessel sequence Bessel multiplier modular Riesz basis

Citation

Khosravi, Amir; Mirzaee Azandaryani, Morteza. Bessel multipliers in Hilbert $C^\ast$--modules. Banach J. Math. Anal. 9 (2015), no. 3, 153--163. doi:10.15352/bjma/09-3-11. https://projecteuclid.org/euclid.bjma/1419001709


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