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Banach Spaces
We consider the notions of linear space, norm, normed linear space (NLS), Banach space. Various examples of Banach spaces are treated. The problems...
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On some special subspaces of a Banach space, from the perspective of best coapproximation
We study the best coapproximation problem in Banach spaces, by using Birkhoff–James orthogonality techniques. We introduce two special types of...
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Banach algebras
In this chapter, we shall introduce Banach algebras and recall their basic properties. General Banach algebras are considered in...
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A Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps
This article describes the surjective linear isometries between spaces of p -times differentiable maps from a domain of the Euclidean space into a...
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Differential Games in a Banach Space without Discrimination
AbstractThe paper is a continuation of author’s research on the existence of an ε-equilibrium in the sense of piecewise program strategies in...
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Discrete-Time Stochastic Calculus in Banach Space
This chapter presents the useful material needed in the sequel, in particular, elements of the martingales and martingale problem in Banach space,...
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Porosity phenomena of non-expansive, Banach space map**s
For any non-trivial convex and bounded subset C of a Banach space, we show that outside of a σ -porous subset of the space of non-expansive map**s C ...
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Banach Space Representations
In this chapter, we present the Schneider-Teitelbaum duality between Banach space representations and Iwasawa modules.
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Relatively compact sets of Banach space-valued bounded-variation spaces
In this paper, we give criteria for the relatively compact sets of Banach space-valued bounded-variation spaces in the sense of Jordan and Banach...
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Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements
In this correspondence, we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements. Most of...
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The adjoint of an operator on a Banach space
Self-adjoint operators in smooth Banach spaces have been already defined in recent works. Here, we extend the concept of adjoint of an operator to...
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Bounded Solutions of Difference Equations in a Banach Space with Asymptotically Constant Operator Coefficient
We study the problem of existence of a unique bounded solution for a difference equation on the half axis with asymptotically constant operator...
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Banach Space Theory
In this chapter we present some basic concepts and results from Functional Analysis (Banach Space Theory). In Sect. 3.2 we introduce the terminology...
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Approximating fixed point results for pseudo-contractive map and some remarks on demi-contractive map in the Banach space
The purpose of our paper is to present a few convergence results for the Krasnoselskii–Mann iteration and also the modified Krasnoselskii–Mann...
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On enriched Hardy–Rogers contractions in Banach space via Krasnoselskij iteration with an application
In this paper we initiate the study of enriched Hardy–Rogers contraction in Banach space and utilize it to establish fixed point results by using the...
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Banach function algebras
In this chapter, we shall concentrate on commutative Banach algebras, especially on commutative, semisimple Banach algebras, identified with Banach...
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Banach Spaces
A normed linear space is a vector space together with a norm function. The norm is like the concept of the length of an arrow. Then, the space admits...
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Banach Spaces
This chapter explores the properties of operators and functionals on general Banach spaces, with the aim of generalizing various results on Hilbert...
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Quasicomplemented Subspaces of Banach Spaces and Separable Quotients
We present a result which generalizes the theorems of Gurariy-Kadets and Lindenstrauss-Rosenthal on quasicomplemented subspaces of Banach spaces. We...
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Banach Algebras
This chapter is an introduction to Banach algebras as an axiomatic approach to the spaces of continuous linear operators on Banach spaces. Their...