Separating Maps and Linear Isometries between Some Spaces of Continuous Functions

Linear Isometries between Subspaces of Continuous Functions

We say that a linear subspace A of C0(X) is strongly separating if given any pair of distinct points x1, x2 of the locally compact space X, then there exists f ∈ A such that |f(x1)| 6= |f(x2)|. In this paper we prove that a linear isometry T of A onto such a subspace B of C0(Y ) induces a homeomorphism h between two certain singular subspaces of the Shilov boundaries of B and A, sending the Cho...

Separating Linear Maps of Continuous Fields of Banach Spaces∗

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Normed Linear Spaces of Continuous Functions

1. Introduction. In addition to its well known role in analysis, based on measure theory and integration, the study of the Banach space B(X) of real bounded continuous functions on a topological space X seems to be motivated by two major objectives. The first of these is the general question as to relations between the topological properties of X and the properties (algebraic, topological, metr...

The Isometries of Some Function Spaces