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 defin...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.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10571113 10871224)+2 种基金the Science and Technology Program of Shaanxi Province (Grant No. 2009JM1011)the Fundmental Research Funds forthe Central Universities (Grant Nos. GK201002006 GK201002012)
文摘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.