Search

The aim of this article is to prove a representation theorem for orthogonally additive polynomials in the spirit of the recent theorem on representation of orthogonally additive polynomials on Banach lattices but for the setting of Riesz spaces. To this purpose the notion of p-orthosymmetric multilinear form is introduced and it is shown to be equivalent to the orthogonally additive property of the corresponding polynomial. Then the space of positive orthogonally additive polynomials on an Archimedean Riesz space taking values on an uniformly complete Archimedean Riesz space is shown to be isomorphic to the space of positive linear forms on the n-power in the sense of Boulabiar and Buskes of the original Riesz space., MEC, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Song-Jian Han., Thesis (M.Phil.)--Chinese University of Hong Kong, 1994., Includes bibliographical references (leaves 72-73)., Acknowledgement --- p.i, p.ii, Introduction --- p.iii, Chapter 1 --- Topological Vector Spaces and Elemantary Duality Theory --- p.1, Chapter 1.1 --- Locally Convex Spaces --- p.2, Chapter 1.2 --- Bornological Spaces and Bornological Vector Spaces --- p.4, Chapter 1.3 --- Elementary Properties of Dual Spaces --- p.6, Chapter 1.4 --- Topological Injections and Surjections Bornological Injections and Surjections --- p.10, Chapter 2 --- Locally Convex Riesz Spaces --- p.15, Chapter 2.1 --- Ordered Vector Spaces --- p.15, Chapter 2.2 --- Riesz Space --- p.18, Chapter 2.3 --- Locally Convex Riesz Spaces --- p.20, Chapter 3 --- Half-Full Injections and Half-Decomposable Surjections Half- Full Bornological Injections and Half-Decomposable Bornologi- cal Surjections --- p.24, Chapter 4 --- Operator Modules between Locally Convex Riesz Spaces --- p.35, Chapter 4.1 --- Preliminaries --- p.35, Chapter 4.2 --- Operator Modules and Ideal Cones --- p.37, Chapter 4.3 --- The Half-Full Injective Hull and the Half-Decomposable Bornolog- ical Surjective Hull of Operator Modules Between Locally Convex Riesz Spaces --- p.41, Chapter 4.4 --- Extensions of Operator Modules and Ideal Cones --- p.57, References --- p.72, http://library.cuhk.edu.hk/record=b5888611, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Summary: The Riesz Representation is of great importance in analysis. But in certain situations such as in infinite dimensional Hilbert spaces it fails to apply. Here we present an extensive proof of a relevant generalization using sigma topology as discovered by Edwin Beggs., Thesis (M.S.T.)--Florida Atlantic University, 1993.

Summary: Locally compact spaces having property (B) are introduced. (B) is the property that each bounded subset of the topological vector space K(X) is order bounded. It is shown that there exist spaces X exhibiting (B) that are not paracompact. Also discussed are the consequences of this property for the dual and bidual of K(X) Both show features resembling those from the Banach space case (X compact). Under (B), for example, the bidual of K(X) is Riesz isomorphic to K(Y) for a suitable locally compact space Y. We also introduce doubly bounded Borel functions Bb(X) which are bounded and vanish outside some compact set. Without using the Riesz representation theorem they are imbedded in the bidual of K(X), extending the approach of H. H. Schaefer (19) (20) for compact spaces to locally compact spaces. Further it is shown that the regular Borel measures form a band in the Riesz dual of Bb(X) These results permit to give a topological characterization of regular Borel measures on X, which yields the Riesz representation theorem as well as a distinguishing property of regular Borel measures as fairly immediate consequences. Finally, some relations between Baire and Borel measures are discussed., Thesis (Ph.D.)--Florida Atlantic University, 1992.

by Zhang Xiao-dong., Thesis (M.Ph.)--Chineses University of Hong Kong, 1987., Bibliography: leaves 88-92., http://library.cuhk.edu.hk/record=b5885823, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Thesis (M.Phil.)--Chinese University of Hong Kong., Bibliography: leaf. 29., http://library.cuhk.edu.hk/record=b5886694, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)