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 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
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