scholarly journals Kuelbs–Steadman Spaces for Banach Space-Valued Measures

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1005
Author(s):  
Antonio Boccuto ◽  
Bipan Hazarika ◽  
Hemanta Kalita
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Norm Convergence ◽  
Type Spaces ◽  
Additive Measures

We introduce Kuelbs–Steadman-type spaces ( K S p spaces) for real-valued functions, with respect to countably additive measures, taking values in Banach spaces. We investigate the main properties and embeddings of L q -type spaces into K S p spaces, considering both the norm associated with the norm convergence of the involved integrals and that related to the weak convergence of the integrals.

scholarly journals Banach spaces with property (w)

1993 ◽  
Vol 35 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Denny H. Leung
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Banach Lattice ◽  
Banach Lattices ◽  
Weakly Compact ◽  
Type Spaces

A Banach space E is said to have Property (w) if every operator from E into E' is weakly compact. This property was introduced by E. and P. Saab in [9]. They observe that for Banach lattices, Property (w) is equivalent to Property (V*), which in turn is equivalent to the Banach lattice having a weakly sequentially complete dual. Thus the following question was raised in [9].Does every Banach space with Property (w) have a weakly sequentially complete dual, or even Property (V*)?In this paper, we give two examples, both of which answer the question in the negative. Both examples are James type spaces considered in [1]. They both possess properties stronger than Property (w). The first example has the property that every operator from the space into the dual is compact. In the second example, both the space and its dual have Property (w). In the last section we establish some partial results concerning the problem (also raised in [9]) of whether (w) passes from a Banach space E to C(K, E).

scholarly journals Fixed Point and Weak Convergence Theorems for(α,β)-Hybrid Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Tian-Yuan Kuo ◽  
Jyh-Chung Jeng ◽  
Young-Ye Huang ◽  
Chung-Chien Hong
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Bregman Distance ◽  
Convergence Theorems ◽  
Convergence Problem

We introduce the class of(α,β)-hybrid mappings relative to a Bregman distanceDfin a Banach space, and then we study the fixed point and weak convergence problem for such mappings.

scholarly journals Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chin-Tzong Pang ◽  
Eskandar Naraghirad ◽  
Ching-Feng Wen
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Maximal Monotone Operator ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Convergence Theorems ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

We study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings which was investigated by Martín-Márques et al. (2013). We then prove weak convergence theorems for the sequences produced by the methods. Some application of our results to the problem of finding a zero of a maximal monotone operator in a Banach space is presented. Our results improve and generalize many known results in the current literature.

The Convergence of Series for Various Choices of Sign in Banach Spaces

1975 ◽  
Vol 27 (2) ◽  
pp. 475-480 ◽  
Author(s):  
James Shirey
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Series Expansion ◽  
Norm Convergence ◽  
Convergence Of Series ◽  
Measurable Functions ◽  
Haar Series

1. Let (xn, Xn) denote a basis for a Banach space (X, ∥ • ∥) of measurable functions in (0, 1).It is shown in [2] and [9] that the equivalence of the normsand ∥ • ∥ is equivalent to the unconditionality of the basis (xn, Xn). In [8] a weaker relationship between these norms is exploited to establish the existence of an element of L1(E) for each E ⊂ (0, 1), |£| > 0, whose Haar series expansion is conditionally convergent in the norm of L\(E).In this note, a Lemma of Orlicz [7] is generalized to provide a relationship between , and the changes in sign that are tolerated in without disruption of norm convergence.

scholarly journals Unconditionally converging polynomials on Banach spaces

1995 ◽  
Vol 117 (2) ◽  
pp. 321-331 ◽  
Author(s):  
Manuel Gonz´lez ◽  
Joaquín M. Gutiérrez
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Weak Topology ◽  
Linear Operators ◽  
Null Sequence ◽  
Good Tool ◽  
Image Position ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series

In the study of polynomials acting on Banach spaces, the weak topology is not such a good tool as in the case of linear operators, due to the bad behaviour of the polynomials with respect to the weak convergence. For example,is a continuous polynomial taking a weakly null sequence into a sequence having no weakly Cauchy subsequences. In this paper we show that the situation is not so bad for unconditional series. Recall that is a weakly unconditionally Cauchy series (in short a w.u.C. series) in a Banach space E if for every f ε E* we have that and is an unconditionally converging series (in short an u.c. series) if every subseries is norm convergent.

scholarly journals Banach spaces for which the space of operators has 2𝔠 closed ideals

2021 ◽  
Vol 9 ◽  
Author(s):  
Daniel Freeman ◽  
Thomas Schlumprecht ◽  
András Zsák
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Spaces ◽  
Type Spaces ◽  
The Continuum ◽  
General Conditions

Abstract We formulate general conditions which imply that ${\mathcal L}(X,Y)$ , the space of operators from a Banach space X to a Banach space Y, has $2^{{\mathfrak {c}}}$ closed ideals, where ${\mathfrak {c}}$ is the cardinality of the continuum. These results are applied to classical sequence spaces and Tsirelson-type spaces. In particular, we prove that the cardinality of the set ofclosed ideals in ${\mathcal L}\left (\ell _p\oplus \ell _q\right )$ is exactly $2^{{\mathfrak {c}}}$ for all $1<p<q<\infty $ .

scholarly journals Some remarks on regular Banach spaces

1996 ◽  
Vol 38 (2) ◽  
pp. 243-248 ◽  
Author(s):  
Denny H. Leung
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Weakly Compact ◽  
Bounded Linear ◽  
Type Spaces

A Banach space E is said to be regular if every bounded linear operator from E into E′ is weakly compact. This property was studied in [7, 9] under the name Property (w). In [7], using James type spaces as constructed in [4], examples were given of regular Banach spaces which fail to have weakly sequentially complete duals, answering a question raised in [9]. In this paper, we present some more results concerning the regularity of James type spaces.

scholarly journals On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Numerical Example ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Krasnoselskii Iteration ◽  
Iteration Processes

In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of the Picard and Krasnoselskii iteration processes. Our results are the extension and improvement of many well-known results of the literature.

scholarly journals New Iterative Algorithm for Two Infinite Families of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Fang Zhang ◽  
Huan Zhang ◽  
Yulong Zhang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Weak Convergence Theorem

We introduce a new iterative scheme for finding a common fixed point of two countable families of multivalued quasi-nonexpansive mappings and prove a weak convergence theorem under the suitable control conditions in a uniformly convex Banach space. We also give a new proof method to the iteration in the paper of Abbas et al. (2011).

scholarly journals Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 150
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Dimensional Algebra ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Linear Subspaces ◽  
Infinite Dimensional Banach Space

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.

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