In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some pr...In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).展开更多
In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C＊-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to eac...In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C＊-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using .A-valued linear bounded operator U ： H → l^2（.A）, V＊U = I, a coustructing method of dual weak frame {xj^＊ ： j ∈ H} for a given weak frame {Xj ： j ∈ J} is obtained. Moreover, pseudo frame decompositions for 74 is given.展开更多
基金The NSF(11271148,11561057)of Chinathe NSF(20151BAB201007)of Jiangxi Provincethe Science and Technology Project(GJJ151061)of Jiangxi Education Department
文摘In this note, we establish a new characterization on g-frames in Hilbert C;-modules from the operator-theoretic point of view, with which we provide a correction to one result recently obtained by Yao(Yao X Y. Some properties of g-frames in Hilbert C;-modules（in Chinese）. Acta Math. Sinica, 2011, 54（1）: 1–8.).
基金Supported by the Emphasis Supported Subject Foundation of Shanxi Province（20055026） Supported by the Emphasis Science Foundation of Yuncheng University（20060103）
文摘In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C＊-module 74, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using .A-valued linear bounded operator U ： H → l^2（.A）, V＊U = I, a coustructing method of dual weak frame {xj^＊ ： j ∈ H} for a given weak frame {Xj ： j ∈ J} is obtained. Moreover, pseudo frame decompositions for 74 is given.
