#### Event Title

Examples of the Stone-Cech Compactification and the Gelfand Transform

#### Location

Diamond 344

#### Start Date

30-4-2015 11:00 AM

#### End Date

30-4-2015 11:55 AM

#### Project Type

Presentation

#### Description

The Gelfand Theorem states that the Gelfand transform between C*-algebra a is an isometric isomorphism, and the proof for this theorem is quite short. How does is this applicable? Are there any classic examples? What about other examples of C*-algebras and their properties which are the basis for Gelfand's theorem? Through examples and further research into the Stone-Cech compactification, I provide insight into why the Gelfand transform is useful and how mathematicians make use of it, and the Stone-Cech compactification.

#### Faculty Sponsor

Ben Mathes

#### Sponsoring Department

Colby College. Mathematics and Statistics Dept.

#### CLAS Field of Study

Natural Sciences

#### Event Website

http://www.colby.edu/clas

#### ID

1665

Examples of the Stone-Cech Compactification and the Gelfand Transform

Diamond 344

The Gelfand Theorem states that the Gelfand transform between C*-algebra a is an isometric isomorphism, and the proof for this theorem is quite short. How does is this applicable? Are there any classic examples? What about other examples of C*-algebras and their properties which are the basis for Gelfand's theorem? Through examples and further research into the Stone-Cech compactification, I provide insight into why the Gelfand transform is useful and how mathematicians make use of it, and the Stone-Cech compactification.

http://digitalcommons.colby.edu/clas/2015/program/346