More Properties of the Classes of Hereditarilyp Banach Sequence Spaces (original) (raw)

A Class of Hereditarily ℓ p (c 0 ) Banach Spaces

We extend the class of Banach sequence spaces constructed by Ledari, as presented in "A class of hereditarily ℓ1 Ba-nach spaces without Schur property" and obtain a new class of hereditarily ℓp(c0) Banach spaces for 1 ≤ p < ∞. Some other properties of this spaces are studied.

On dual of Banach sequence spaces

J. Hagler and P. Azimi have introduced a class of Banach sequence spaces, the X α,1 spaces as a class of hereditarily 1 Banach spaces. In this paper, we show that (i) X * α,1 , the dual of Banach space X α,1 contains asymptotically isometric copies of ∞, (ii) X * α,1 is nonseparable although X α,1 is a separable Banach space. Also, we show X α,1 is not hereditarily indecomposable. p. Here, using two methods we show that the Banach spaces X * α,1 , the dual of Banach spaces X α,1 , are nonseparable. By the first method, we show X * α,1 contain asymptotically isometric copy of ∞. A result of [6] shows that X * α,1 contain isometric copy of ∞ , and then they are nonseparable. By the second method,

On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I

Filomat, 2011

In the present paper, which is a natural continuation of the work done in [13], we determine the α-, β-and γ-duals of the sequence spaces λ p and λ ∞ of non-absolute type, where 1 ≤ p < ∞. Further, we characterize some related matrix classes and deduce the characterizations of some other classes by means of a given basic lemma.

On Some New Sequence Spaces of non absolute type related to the Spaces

In the present paper we determine the  ,  and  duals of the sequence spaces 2 p  and 2    of non absolute type, 1 p<  . Further we characterize some related matrix classes and deduce the characterization of some other classes by means of a given in basic lemma. Key words : Sequence spaces, BK-spaces  ,  ,  duals, matrix mappings.

On Some Sequence Spaces Related to a Sequence in a Normed space

2019

In this paper, we introduce some new multiplier sequence spaces by using sequences in a normed space XXX and matrix domain of Ces\'aro summability method in ellinfty\ell_\inftyellinfty and c_0c_0c_0. Then we obtain the characterizations of completeness and barrelledness of normed space XXX through its weakly and weakly* unconditionally Cauchy series.

Some New Cauchy Sequence Spaces

Universal Journal of Mathematics and Applications

In this paper, our goal is to introduce some new Cauchy sequence spaces. These spaces are defined by Cauchy transforms. We shall use notations C ∞ (s,t), C (s,t) and C 0 (s,t) for these new sequence spaces. We prove that these new sequence spaces C ∞ (s,t), C (s,t) and C 0 (s,t) are the BK−spaces and isomorphic to the spaces l ∞ , c and c 0 , respectively. Besides the bases of these spaces, α−, β − and γ− duals of these spaces will be given. Finally, the matrix classes (C (s,t) : l p) and (C (s,t) : c) have been characterized.

Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces

Bulletin of the Belgian Mathematical Society - Simon Stevin

The Fréchet (resp., (LB)-) sequence spaces ces(p+) := r>p ces(r), 1 ≤ p < ∞ (resp. ces(p-) := 1<r<p ces(r), 1 < p ≤ ∞), are known to be very different to the classical sequence spaces ℓ p+ (resp., ℓ p-). Both of these classes of non-normable spaces ces(p+), ces(p-) are defined via the family of reflexive Banach sequence spaces ces(p), 1 < p < ∞. The dual Banach spaces d(q), 1 < q < ∞, of the discrete Cesàro spaces ces(p), 1 < p < ∞, were studied by G. Bennett, A. Jagers and others. Our aim is to investigate in detail the corresponding sequence spaces d(p+) and d(p-), which have not been considered before. Some of their properties have similarities with those of ces(p+), ces(p-) but, they also exhibit differences. For instance, ces(p+) is isomorphic to a power series Fréchet space of order 1 whereas d(p+) is isomorphic to such a space of infinite order. Every space ces(p+), ces(p-) admits an absolute basis but, none of the spaces d(p+), d(p-) have any absolute basis.

On a certain class of Banach spaces

Topology and its Applications, 2013

Using a strengthening of the concept of K σδ set, introduced in this paper, we study a certain subclass of the class of K σδ Banach spaces; the so called strongly K σδ Banach spaces. This class of spaces includes subspaces of strongly weakly compactly generated (SWCG) as well as Polish Banach spaces and it is related to strongly weakly Kanalytic (SWKA) Banach spaces as the known classes of K σδ and weakly K-analytic (WKA) Banach spaces are related.

Some -Type New Sequence Spaces and Their Geometric Properties

Abstract and Applied Analysis, 2009

We introduce an p -type new sequence space and investigate its some topological properties including AK and AD properties. Besides, we examine some geometric properties of this space concerning Banach-Saks type p and Gurarii's modulus of convexity.