نتایج جستجو برای: Banach frame
تعداد نتایج: 116943 فیلتر نتایج به سال:
In this article, we consider pair frames in Banach spaces and introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as special kinds of (Banach) pair frames. Some frame-like inequalities for (Banach) pair frames are presented. The elements that participant in the construction of (Ba...
motivating the perturbations of frames in hilbert and banach spaces, in this paper we introduce the invariance of fr'echet frames under perturbation. also we show that for any fr'echet spaces, there is a fr'echet frame and any element in these spaces has a series expansion.
let h be a separable hilbert space and let b be the set of bessel sequences in h. by using several interesting results in operator theory we study some topological properties of frames and riesz bases by constructing a banach space structure on b. the convergence of a sequence of elements in b is de_ned and we determine whether important properties of the sequence is preserved under the con...
the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.
For a fusion Banach frame ({Gn, vn}, S) for a Banach space E, if ({v∗ n(E), v∗ n}, T ) is a fusion Banach frame for E∗, then ({Gn, vn}, S; {v∗ n(E), v∗ n}, T ) is called a fusion bi-Banach frame for E. It is proved that if E has an atomic decomposition, then E also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a chara...
The Banach frame for a Banach space can reconstruct each vector in by the pre-frame operator or the reconstruction operator. The Banach Λ-frame for operator spaces was introduced by Kaushik, Vashisht and Khattar [Reconstruction Property and Frames in Banach Spaces, Palestine Journal of Mathematics, 3(1), 2014, 11-26]. In this paper we give necessary and sufficient conditions for the existen...
A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if X is a Banach space such that X ∗ has a SRBF, then X has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space X has an approximative Schauder frame, then X ∗ has a SRBF. Finally, the existence of a non-lin...
The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an $tilde{X}$-frame and a system conjugate to $tilde{X}$-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of $tilde{X}$-frame having a conjugate system is studied.
Retro Banach Frames, Almost Exact Retro Banach Frames in Banach Spaces (communicated by Oleg Reinov)
In this paper, we give characterizations of retro Banach frames in Banach spaces. The notion of almost exact retro Banach frame is defined and a characterization of retro Banach frame has been given. Also results exhibiting relationship between frames, almost exact retro Banach frames and Riesz bases has been proved. Finally, we give some perturbation results of retro Banach frames and an almos...
We analyze the construction of a sequence space Θ̃, resp. a sequence of sequence spaces, in order to have {gi} ∞ i=1 as a Θ̃-frame or Banach frame for a Banach space X , resp. pre-F -frame or F -frame for a Fréchet space XF = ∩s∈N0Xs, where {Xs}s∈N0 is a sequence of Banach spaces.
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