We begin by looking at why operator spaces are necessary in the study of operator algebras and many examples of and ways to construct operator algebras. Then we examine how certain basic algebraic relationships break down when norms are placed on them. This leads to ways to correct these ideas using matrix norms.

Author Bio

Currently, I am an undergraduate attending the University of Nebraska - Lincoln majoring in mathematics withminors in computer science and physics. During the summer of 2001, I participated in an REU at the University ofHouston. While there, under the direction of Dr. Blecher, I researched concepts involved with operator algebra andwrote the paper I have submitted to this journal. I am currently continuing research in this area while at Nebraskaand hope to develop it into an undergraduate thesis. Pure mathematics, in particular operator algebra, is myprimary mathematical interest but I still hope to explore other avenues. After graduation, tentatively planned for thespring of 2003, I plan to pursue a masters and possible PhD. in mathematics. In my spare time I enjoy attendingnumerous concerts, plays, and movies.