Modular frames and invertibility of multipliers in Hilbert C*-modules

ABSTRACT

We investigate some properties for Hilbert $C^{\ast }$-modular frames. In the present paper, we also investigate some conditions for invertibility of multipliers in Hilbert $C^{\ast }$-module spaces. We show that by appropriate conditions for symbols, the inverse of an invertible frame multiplier can be represented as a frame multiplier. Dual frames play important role in this representation. We prove and generalize some of the results obtained for frames in Hilbert spaces to Hilbert $C^{\ast }$-modules.

KEYWORDS:

• Frame
• multiplier
• Hilbert $C^{\ast }$-module
• Riesz basis

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary: 46L08
• Secondary: 42C15
• 46H25
• 47A05

Acknowledgements

The authors are very thankful to the referee for valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.