Let H be a separable Hilbert space, BH（I）, B（H） and K（H） the sets of all Bessel sequences {fi}i∈I in H, bounded linear operators on H and compact operators on H, respectively. Two kinds of multiplications and i...Let H be a separable Hilbert space, BH（I）, B（H） and K（H） the sets of all Bessel sequences {fi}i∈I in H, bounded linear operators on H and compact operators on H, respectively. Two kinds of multiplications and involutions are introduced in light of two isometric linear isomorphisms αH： BH（I）→ B（l2）,β ： BH（I） → B（H）, respectively, so that BH（I） becomes a unital C＊-algebra under each kind of multiplication and involution. It is proved that the two C＊-algebras （BH（I）, o, #） and （BH（I）, ., ＊） are ＊-isomorphic. It is also proved that the set FH （I） of all frames for H is a unital multiplicative semi-group and the set RH（I） of all Riesz bases for H is a self-adjoint multiplicative group, as well as the set KH （I） ：=β-1 （K（H）） is the unique proper closed self-adjoint ideal of the C＊-algebra BH （I）.展开更多
The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient co...The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient conditions for the finite extensions of generalizedBessel sequences to generalized frames or tight generalized frames are provided, and everyresult is illustrated by the corresponding example.展开更多
Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel seq...Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these 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 National Natural Science Foundation of China(Grant Nos.1140135911371012+2 种基金11301318)China Postdoctoral Science Foundation(Grant No.2014M552405)the Natural Science Research Program of Shaanxi Province(Grant No.2014JQ1010)
文摘Let H be a separable Hilbert space, BH（I）, B（H） and K（H） the sets of all Bessel sequences {fi}i∈I in H, bounded linear operators on H and compact operators on H, respectively. Two kinds of multiplications and involutions are introduced in light of two isometric linear isomorphisms αH： BH（I）→ B（l2）,β ： BH（I） → B（H）, respectively, so that BH（I） becomes a unital C＊-algebra under each kind of multiplication and involution. It is proved that the two C＊-algebras （BH（I）, o, #） and （BH（I）, ., ＊） are ＊-isomorphic. It is also proved that the set FH （I） of all frames for H is a unital multiplicative semi-group and the set RH（I） of all Riesz bases for H is a self-adjoint multiplicative group, as well as the set KH （I） ：=β-1 （K（H）） is the unique proper closed self-adjoint ideal of the C＊-algebra BH （I）.
基金partially supported by the National Natural Science Foundation of China(61471410)
文摘The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient conditions for the finite extensions of generalizedBessel sequences to generalized frames or tight generalized frames are provided, and everyresult is illustrated by the corresponding example.
基金Supported by the Doctoral Research Project of Yan’an University(Grant No.YDBK2017-21)the Foundation of Yan’an University(Grant No.YDQ2018-09)
文摘Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these 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.
