scholarly journals Ideal convergence characterization of the completion of linear n-normed spaces

2011 ◽  
Vol 61 (3) ◽  
pp. 683-689 ◽  
Author(s):  
A. Şahiner ◽  
M. Gürdal ◽  
T. Yiğit
Keyword(s):  
Normed Spaces ◽  
Ideal Convergence

scholarly journals Ideal Convergence and Completeness of a Normed Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 897 ◽  
Author(s):  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
María del Pilar Romero de la Rosa ◽  
Antonio Sala
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Convergence Space ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Underlying Space ◽  
Phd Thesis

We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.

Λ-strongly summable sequence spaces in n-normed spaces defined by ideal convergence and an Orlicz function

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Ayhan Esi ◽  
M. Kemal Özdemir
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Summable Sequence ◽  
Inclusion Results

AbstractIn this paper we introduce some certain new sequence spaces via ideal convergence, λ-sequence and an Orlicz function in n-normed spaces and study different properties of these spaces and also establish some inclusion results among them.

scholarly journals Some Generalized Difference Sequence Spaces Defined by a Sequence of Moduli inn-Normed Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi ◽  
Kuldip Raj ◽  
S. A. Mohiuddine
Keyword(s):  
Sequence Spaces ◽  
Infinite Matrix ◽  
Difference Sequence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce some new generalized difference sequence spaces by means of ideal convergence, infinite matrix, and a sequence of modulus functions overn-normed spaces. We also make an effort to study several properties relevant to topological, algebraic, and inclusion relations between these spaces.

scholarly journals Generalized Differenceλ-Sequence Spaces Defined by Ideal Convergence and the Musielak-Orlicz Function

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Awad A. Bakery
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
The Ideal

We introduced the ideal convergence of generalized difference sequence spaces combining an infinite matrix of complex numbers with respect toλ-sequences and the Musielak-Orlicz function overn-normed spaces. We also studied some topological properties and inclusion relations between these spaces.

scholarly journals Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Saeed Sarabadan ◽  
Sorayya Talebi
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Convergence Of Sequences

We present various kinds of statistical convergence andℐ-convergence for sequences of functions with values in 2-normed spaces and obtain a criterion forℐ-convergence of sequences of functions in 2-normed spaces. We also define the notion ofℐ-equistatistically convergence and studyℐ-equi-statistically convergence of sequences of functions.

scholarly journals Multipliers of Modules of Continuous Vector-Valued Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liaqat Ali Khan ◽  
Saud M. Alsulami
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Normed Spaces ◽  
Locally Compact ◽  
Continuous Vector ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space ◽  
Locally Convex

In 1961, Wang showed that ifAis the commutativeC*-algebraC0(X)withXa locally compact Hausdorff space, thenM(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing thatHomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)),whereEandFarep-normed spaces which are also essential isometric leftA-modules withAbeing a certain commutativeF-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

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