scholarly journals New Sequence Spaces and Function Spaces on Interval[0,1]

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Cheng-Zhong Xu ◽  
Gen-Qi Xu
Keyword(s):  
Banach Spaces ◽  
Function Spaces ◽  
Summation Method ◽  
Sequence Spaces ◽  
Polynomial Space ◽  
And Function

We study the sequence spaces and the spaces of functions defined on interval0,1in this paper. By a new summation method of sequences, we find out some new sequence spaces that are interpolating into spaces betweenℓpandℓqand function spaces that are interpolating into the spaces between the polynomial spaceP0,1andC∞0,1. We prove that these spaces of sequences and functions are Banach spaces.

scholarly journals On Certain Topological Properties of Normed Space Valued Null Function Space c0 (S, (E, || . || ), xi, u) and Its Paranormed Structure

2015 ◽  
Vol 15 (1) ◽  
pp. 121-128
Author(s):  
Narayan Prasad Pahari
Keyword(s):  
Functional Analysis ◽  
Function Space ◽  
Normed Space ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Basic Sequence ◽  
Topological Properties ◽  
New Class ◽  
And Function ◽  
Class Of Functions

The aim of this paper is to introduce and study a new class c0 (S, (E, || . || ), ξ, u) of normed space E valued functions which will generalize some of the well known  basic sequence spaces and function spaces studied in Functional Analysis.. Beside the investigation pertaining to the linear paranormed structure of the class c0 ( S, (E, || . || ), ξ, u ) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class c0 (S, (E, || . || ), ξ, u) in terms of different ξ and u so that such a class of functions is contained in or equal to another class of similar nature.DOI: http://dx.doi.org/10.3126/njst.v15i1.12028Nepal Journal of Science and TechnologyVol. 15, No.1 (2014) 121-128

CHAOTIC POLYNOMIALS ON SEQUENCE AND FUNCTION SPACES

2010 ◽  
Vol 20 (09) ◽  
pp. 2861-2867 ◽  
Author(s):  
F. MARTÍNEZ-GIMÉNEZ ◽  
A. PERIS
Keyword(s):  
Chaotic Dynamics ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Arbitrary Degree ◽  
And Function

We study chaos in the sense of Devaney for two models of polynomials (homogeneous and non-homogeneous) of arbitrary degree, defined on certain sequence spaces. Consequences are also obtained for the chaotic dynamics of the corresponding polynomials on some function spaces.

scholarly journals The Bishop-Phelps-Bollobàs Property for Compact Operators

2018 ◽  
Vol 70 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Sheldon Dantas ◽  
Domingo García ◽  
Manuel Maestre ◽  
Miguel Martín
Keyword(s):  
Hilbert Space ◽  
Topological Space ◽  
Banach Spaces ◽  
Positive Measure ◽  
Compact Operators ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Nikodym Property

AbstractWe study the Bishop-Phelps-Bollobàs property (BPBp) for compact operators. We present some abstract techniques that allow us to carry the BPBp for compact operators from sequence spaces to function spaces. As main applications, we prove the following results. Let X and Y be Banach spaces. If (c0, Y) has the BPBp for compact operators, then so do (C0(L), Y) for every locally compactHausdorò topological space L and (X, Y) whenever X* is isometrically isomorphic to . If X* has the Radon-Nikodým property and (X), Y) has the BPBp for compact operators, then so does (L1(μ, X), Y) for every positive measure μ; as a consequence, (L1(μ, X), Y) has the BPBp for compact operators when X and Y are finite-dimensional or Y is a Hilbert space and X = c0 or X = Lp(v) for any positive measure v and 1 < p < ∞. For , if (X, (Y)) has the BPBp for compact operators, then so does (X, Lp(μ, Y)) for every positive measure μ such that L1(μ) is infinite-dimensional. If (X, Y) has the BPBp for compact operators, then so do (X, L∞(μ, Y)) for every σ-finite positive measure μ and (X, C(K, Y)) for every compact Hausdorff topological space K.

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

Convexity of integral transforms and function spaces

2007 ◽  
Vol 18 (1) ◽  
pp. 1-14 ◽  
Author(s):  
R. Balasubramanian ◽  
S. Ponnusamy ◽  
D. J. Prabhakaran
Keyword(s):  
Integral Transforms ◽  
Function Spaces ◽  
And Function

Upper lp-estimates in vector sequence spaces, with some applications

1993 ◽  
Vol 113 (2) ◽  
pp. 329-334 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Fernando Sánchez
Keyword(s):  
Banach Spaces ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Vector Sequence ◽  
Lp Estimates ◽  
Banach Sequence Space ◽  
Banach Sequence

In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

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