Files in this item
Files | Description | Format |
---|---|---|
application/pdf ![]() ![]() | (no description provided) |
Description
Title: | Local Structure of Operator Algebras |
Author(s): | Amini, Massoud |
Doctoral Committee Chair(s): | Ruan, Zhong-Jin |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
Abstract: | In this thesis some aspects of a local theory for operator algebras are explored. The main purpose is to provide some tools for studying locally compact quantum groups. We first consider inverse limits of $C\sp*$-algebras (pro-$C\sp*$-algebras); among them are the multipliers of the Pedersen ideal of a $C\sp*$-algebra. We distinguish these as locally compact pro-$C\sp*$-algebras and give a characterization of all locally compact $\sigma$-$C\sp*$-algebras. We show that in the commutative case, the locally compact $\sigma$-$C\sp*$-algebras are exactly those which correspond to locally compact Hausdorff topological spaces. Also we characterize these multipliers among the elements affiliated with the corresponding $C\sp*$-algebra. As an application, we prove a version of the generalized Stone's theorem, and apply it to show that certain differential operators are affiliated with the group $C\sp*$-algebras of Lie groups. Then we turn to inverse limits of $W\sp*$-algebras and use the techniques of non-commutative topology to study the local structure of Kac algebras. Also we study inverse limits of Kac algebras. |
Issue Date: | 1998 |
Type: | Text |
Language: | English |
Description: | 86 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998. |
URI: | http://hdl.handle.net/2142/86956 |
Other Identifier(s): | (MiAaPQ)AAI9834650 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 1998 |
This item appears in the following Collection(s)
-
Dissertations and Theses - Mathematics
-
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois