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.
Hain, Seth M.
"Algebra and Matrix Normed Spaces,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 2
, Article 5.
Available at: http://scholar.rose-hulman.edu/rhumj/vol2/iss2/5