Preservation of the Norms of Linear Operators Acting on Some Quaternionic Function Spaces

2005 ◽  
pp. 205-220 ◽  
Author(s):  
M. Elena Luna-Elizarrarás ◽  
Michael Shapiro
Keyword(s):  
Function Spaces ◽  
Linear Operators

scholarly journals Positive operators and approximation in function spaces on completely regular spaces

2003 ◽  
Vol 2003 (61) ◽  
pp. 3841-3871 ◽  
Author(s):  
Francesco Altomare ◽  
Sabrina Diomede
Keyword(s):  
Natural Extension ◽  
Function Spaces ◽  
Positive Operators ◽  
Linear Operators ◽  
Topological Spaces ◽  
Approximation Properties ◽  
Completely Regular ◽  
Borel Measures ◽  
Korovkin Type Theorems ◽  
Locally Convex

We discuss the approximation properties of nets of positive linear operators acting on function spaces defined on Hausdorff completely regular spaces. A particular attention is devoted to positive operators which are defined in terms of integrals with respect to a given family of Borel measures. We present several applications which, in particular, show the advantages of such a general approach. Among other things, some new Korovkin-type theorems on function spaces on arbitrary topological spaces are obtained. Finally, a natural extension of the so-called Bernstein-Schnabl operators for convex (not necessarily compact) subsets of a locally convex space is presented as well.

scholarly journals Translation-invariant linear operators

1993 ◽  
Vol 113 (1) ◽  
pp. 161-172
Author(s):  
H. G. Dales ◽  
A. Millinoton
Keyword(s):  
Linear Operator ◽  
Canonical Form ◽  
Function Spaces ◽  
Linear Operators ◽  
Translation Invariant ◽  
Continuous Operators

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, ℝ or ℝ+ which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous operators. In some cases each such operator is zero. The second problem is essentially the ‘multiplier problem’, and it has been extensively discussed; see [7], for example.

scholarly journals REPRESENTATION THEOREMS OF LINEAR OPERATORS ON P-ADIC FUNCTION SPACES

2004 ◽  
Vol 23 (2) ◽  
Author(s):  
JOSE AGUAYO ◽  
ELSA CHANDIA ◽  
JACQUELINE OJEDA
Keyword(s):  
Function Spaces ◽  
Linear Operators ◽  
Representation Theorems
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