R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual...R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.展开更多
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 Scientific Research Start-up Foundation of Fuzhou University,China(Grant No.022410)the Science and Technology Funds from Fuzhou University,China(Grant No.2012-XQ-29)the Natural Science Foundation of Fujian Province,China(Grant No.2012J01005)
文摘R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.
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.
