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Integral Equations and Operator Theory

, Volume 68, Issue 2, pp 193–205 | Cite as

Multipliers for p-Bessel Sequences in Banach Spaces

  • Asghar Rahimi
  • Peter Balazs
Article

Abstract

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.

Mathematics Subject Classification (2010)

Primary 42C15 Secondary 41A58 47A58 

Keywords

p-Bessel sequence p-Riesz sequence (p, q)-Bessel multiplier (r, p, q)-nuclear operators 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MaraghehMaraghehIran
  2. 2.Acoustics Research Institute, Austrian Academy of SciencesViennaAustria

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