#### Date of Award

Fall 1999

#### Project Type

Dissertation

#### Program or Major

Mathematics

#### Degree Name

Doctor of Philosophy

#### First Advisor

Don Hadwin

#### Abstract

We study central sequences of C*-algebras. We find connections of the central sequences of a C*-algebra and its representations. More specifically, we prove the following results: (a) Characterization of central sequences in certain C*-subalgebras of C(X, Mn), where X is a compact Hausdorff space. We also state the conditions under which central sequences are trivial/hypercentral. (b) A representation of the C*-algebra is in the point norm closure of the set of all equivalence classes of irreducible representation if and only if it is multiplicity free. (c) For a C*-algebra A, all of whose representations are bounded by some fixed number, the following are equivalent: (1) A is a continuous trace C*-algebra. (2) Every central sequence in A is trivial. (3) Irr(A, Mn) is point norm closed in Rep(A, Mn). (4) A can be written as a finite direct sum of C*-algebras of the form C( X, Mn, ∼, beta) where ∼ is an equivalence relation on X and beta:∼→ Un. Un is the set of n x n unitary matrices.

#### Recommended Citation

Pendharkar, Hemant, "Central sequences and C*-algebras" (1999). *Doctoral Dissertations*. 2098.

https://scholars.unh.edu/dissertation/2098