In this paper we introduce and study some new sequence spaces.

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...

In this article we define some difference sequence spaces using a new difference operator. We show that these spaces can be made BK-spaces under a suitable norm. We also find their isometrically isomorphic spaces and thus we find the dual of some of the spaces. Furthermore we study the spaces for separable space, reflexive space, Hilbert space and investigate for solid space, symmetric space, m...

The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation). In order to avoid serious technical difficulties, the order of the jet spa...

In the present paper we introduce the sequence spaces defined by a sequence of modulus function F = (fk) in n-normed spaces. We study some topological properties and prove some inclusion relations between these spaces.

The dual spaces $d(p), 1 \lt p \infty ,$ of the discrete Cesaro (Banach) $\mathrm{ces} (q)$, $1 q were studied by G. Bennett, A. Jagers and others. These (reflexive) Banach induce non-normable Frechet $d (p+) := \bigcap_{r \gt p} d (r), $ for \leq (LB)-spaces (p-) \bigcup_{ r } recently introduced investigated in [11]. Here a detailed study is made various aspects, such as spectrum, continuity,...

The Fréchet $(\mbox{resp.}, (\mbox{LB})\mbox{-})$ sequence spaces $ces(p+) := \bigcap_{r > p} ces(r), 1 \leq p < \infty $ (resp. ces (p\mbox{-}) \bigcup_{ r (r), \infty),$ are known to be very different the classical \ell_ {p+} (resp., \ell_{p_{\mbox{-}}}).$ Both of these classes non-normable (p+), (p\mbox{-})$ defined via family reflexive Banach (p), .$ \textit{dual}\/ d (q), q ,$ discrete Ces...

We study N-term approximation for general families of sequence spaces, establishing sharp versions of Jackson and Bernstein inequalities. The sequence spaces used are adapted to provide characterizations of Triebel-Lizorkin and Besov spaces by means of wavelet-like systems using general dilation matrices, and thus they include spaces of anisotropic smoothness. As an application we characterize ...

We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...

The idea of single difference sequence spaces was introduced by Kizmaz and this concept was generalized by various authors. In this paper, we define the sequence spaces χ2 (∆u,Mmn, p, s) and Λ2 (∆ γ u,Mmn, p, s) , where M = (Mmn) is a sequence of modulus functions, and examine some inclusion relations and properties of these spaces. 2000 Mathematics Subject Classification: 40A05,40C05,40D05.