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
The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α opera...The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given.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.
基金Supported by National Natural Science Foundation of China(Grant Nos.11171197,11371012)the Fundamental Research Funds for the Central Universities(Grant No.GK201301007)
文摘The aim of this paper is to establish a series of important properties of local Lipschitz-α mappings from a subset of a normed space into a normed space. These mappings include Lipschitz operators, Lipschitz-α operators and local Lipschitz functions. Some applications to the theory of sublinear expectation spaces are given.
