Search
Search Results
-
Banach algebras
In this chapter, we shall introduce Banach algebras and recall their basic properties. General Banach algebras are considered in...
-
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...
-
Banach Spaces
This chapter explores the properties of operators and functionals on general Banach spaces, with the aim of generalizing various results on Hilbert...
-
Banach function algebras
In this chapter, we shall concentrate on commutative Banach algebras, especially on commutative, semisimple Banach algebras, identified with Banach...
-
Banach limit, fixed points and Ulam stability
We show how to use the Banach limit to obtain a fixed point theorem for function spaces. We also present some applications of this result in Ulam...
-
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...
-
Hahn–Banach Theorem
The notion of extension in continuity of a linear continuous functional is introduced an famous Hahn-Banach theorem is formulated, together with...
-
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...
-
Hahn-Banach Theorems
The analytic form of the Hahn-Banach theorem concerns the extension of linear functionals defined on a subspace of a normed linear space to the...
-
Direct limits in categories of normed vector lattices and Banach lattices
After collecting a number of results on interval and almost interval preserving linear maps and vector lattice homomorphisms, we show that direct...
-
Banach algebras on locally compact groups
In this chapter, we shall consider the classical Banach algebras of harmonic analysis that are associated with a locally compact group G. The class...
-
Boolean Valued Analysis of Banach Spaces
We implement the Boolean valued analysis of Banach spaces. The realizations of Banach spaces in a Boolean valued universe are lattice normed spaces....
-
On Limit Theorems for Functional Autoregressive Processes with Random Coefficients
AbstractIn this paper we consider a Banach space valued random coefficient autoregressive process. Our studies on this process involve existence,...
-
Differentiation in Banach Spaces
In a Banach space, all the necessary ingredients are present for the study of calculus on the space. This topic of differentiation on Banach space is...
-
Application of Banach limits to invariant measures of infinite-dimensional Hamiltonian flows
Applying an invariant measure on phase space, we study the Koopman representation of a group of symplectomorphisms in an infinite-dimensional Hilbert...
-
Projective Spectrum in Banach Algebras
Consider a Banach algebra \({\mathcal B}\) with unit I. The classical...
-
On the Properties of Quasi-Banach Function Spaces
In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they possess...
-
Approximation of generalized derivation in quasi-Banach algebras
Motivated by the notion of the Hyers–Ulam stability, we will first study the stability problem of a certain class of functional inequalities...
-
On the Lipschitz numerical index of Banach spaces
In this article, we investigate further on the Lipschitz numerical radius and index which were recently introduced. First, we provide some renorming...