Multipliers for p-Bessel sequences in Banach spaces

Details Multipliers for p-Bessel sequences in Banach spaces Multipliers for p-Bessel sequences in Banach spaces

2010-04-29

arxiv.org/abs/1004.5212v1

Integral Equations and Operator Theory, Volume 68 (2), 193-205 (2010)

Mathematics

Functional Analysis

17 pages

Scientific paper

10.1007/s00020-010-1814-7

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.

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