Date of Award
2006
Publication Type
Master Thesis
Degree Name
M.Sc.
Department
Mathematics and Statistics
Keywords
Mathematics.
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Abstract
This thesis explores a possible operator space framework for the study of the second dual of a Banach algebra A. We prove some new characterizations for A to be Arens regular and we try to unify, for the Arens regularity problem, two of current approaches: by considering weakly almost periodic functionals on A and by considering the topological center of A**. Motivated by this study, we define two operator space tensor products, namely, the extended projective tensor product and the normal projective tensor product. We investigate the properties of these two products, and compare them with other operator space tensor products. It is shown that the extended projective tensor product is injective, and the normal projective tensor product can linearize a class of bilinear maps under the condition that the pair of operator spaces has certain type of Kaplansky density property.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2006 .C366. Source: Masters Abstracts International, Volume: 45-01, page: 0332. Thesis (M.Sc.)--University of Windsor (Canada), 2006.
Recommended Citation
Cao, Haiping, "Operator space tensor products and the second dual of a Banach algebra." (2006). Electronic Theses and Dissertations. 2935.
https://scholar.uwindsor.ca/etd/2935