Mackey Topologies and Mixed Topologies in Riesz Spaces

Positivity ◽  
2006 ◽  
Vol 10 (3) ◽  
pp. 591-606 ◽  
Author(s):  
Jurie Conradie
Keyword(s):  
Riesz Spaces ◽  
Mackey Topologies

scholarly journals Correction to: Disjointness preserving operators on normed pre-Riesz spaces: extensions and inverses

Positivity ◽  
2020 ◽  
Vol 24 (2) ◽  
pp. 505-505
Author(s):  
Anke Kalauch ◽  
Onno van Gaans ◽  
Feng Zhang
Keyword(s):  
Riesz Spaces ◽  
Disjointness Preserving

scholarly journals Extending Edgar's ordering to locally convex spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 175-188
Author(s):  
Neill Robertson
Keyword(s):  
Convex Space ◽  
Dual Pair ◽  
Locally Convex Space ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Hausdorff Topological Vector Space ◽  
Locally Convex ◽  
Mackey Topologies

By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively.

Small Riesz spaces

1989 ◽  
Vol 105 (3) ◽  
pp. 523-536 ◽  
Author(s):  
G. Buskes ◽  
A. van Rooij
Keyword(s):  
Representation Theory ◽  
Direct Method ◽  
Riesz Space ◽  
Pictorial Representation ◽  
Representation Theorems ◽  
Riesz Spaces ◽  
Number Of Authors

Many facts in the theory of general Riesz spaces are easily verified by thinking in terms of spaces of functions. A proof via this insight is said to use representation theory. In recent years a growing number of authors has successfully been trying to bypass representation theorems, judging them to be extraneous. (See, for instance, [9,10].) In spite of the positive aspects of these efforts the following can be said. Firstly, avoiding representation theory does not always make the facts transparent. Reading the more cumbersome constructions and procedures inside the Riesz space itself one feels the need for a pictorial representation with functions, and one suspects the author himself of secret heretical thoughts. Secondly, the direct method leads to repeating constructions of the same nature over and over again.

scholarly journals A Fubini Theorem in Riesz spaces for the Kurzweil-Henstock Integral

2011 ◽  
Vol 9 (3) ◽  
pp. 283-304 ◽  
Author(s):  
A. Boccuto ◽  
D. Candeloro ◽  
A. R. Sambucini
Keyword(s):  
Type Theorem ◽  
Riesz Space ◽  
Fubini Theorem ◽  
Real Plane ◽  
Henstock Integral ◽  
Riesz Spaces

A Fubini-type theorem is proved, for the Kurzweil-Henstock integral of Riesz-space-valued functions defined on (not necessarily bounded) subrectangles of the “extended” real plane.

scholarly journals Vector measures and Mackey topologies

2012 ◽  
Vol 23 (1-2) ◽  
pp. 113-122 ◽  
Author(s):  
Marian Nowak
Keyword(s):  
Vector Measures ◽  
Mackey Topologies
Sign in / Sign up

Export Citation Format

Share Document