This is an announcement for the paper "Multipliers for p-Bessel sequences in Banach spaces" by Asghar Rahimi and Peter Balazs.
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.
Archive classification: math.OA math.FA
Mathematics Subject Classification: Primary 42C40, Secondary 41A58, 47A58
Remarks: 17 pages
Submitted from: Peter.Balazs@oeaw.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1004.5212
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