| Stability of (p,Y)-Operator Frames |
| Received:April 03, 2009 Revised:October 14, 2009 |
| Key Words:
p-frame (p,Y)-operator Bessel sequence (p,Y)-operator frame perturbation Banach space.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10571113; 10871224), the Science and Technology Program of Shaanxi Province (Grant No.2009JM1011) and the Fundmental Research Funds for the Central Universities (Grant Nos.GK201002006; GK201002012). |
| Author Name | Affiliation | | Zhi Hua GUO | College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China | | Huai Xin CAO | College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China | | Jun Cheng YIN | College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China
College of Science, China Jiliang University, Zhejiang 310018, P. R. China |
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| Abstract: |
| In this paper we study the stability of $(p,Y)$-operator frames. We firstly discuss the relations between $p$-Bessel sequences (or $p$-frames) and $(p,Y)$-operator Bessel sequences (or $(p,Y)$-operator frames). Through defining a new union, we prove that adding some elements to a given $(p,Y)$-operator frame, the resulted sequence will be still a $(p,Y)$-operator frame. We obtain a necessary and sufficient condition for a sequence of compound operators to be a $(p,Y)$-operator frame. Lastly, we show that $(p,Y)$-operator frames for $X$ are stable under some small perturbations. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.03.020 |
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