Extreme points of the unit ball of an operator space
Abstract
This paper is a revision and an enlargement of the previous version titled "Extreme points of the unit ball of a quasi-multiplier space" which had been circulated since 2004. We study extreme points of the unit ball of an operator space by introducing the new notion (approximate) "quasi-identities". Then we characterize an operator algebra with a contractive approximate quasi- (respectively, left, right, two-sided) identity in terms of quasi-multipliers and extreme points. Furthermore, we give a very neat necessary and sufficient condition for a given operator space to become a -algebra or a one-sided ideal in a -algebra in terms of quasi-multipliers. An extreme point is also used to show that any TRO with predual can be decomposed to the direct sum of a two-sided ideal, a left ideal, and a right ideal in some von Neumann algebra.
Cite
@article{arxiv.math/0408235,
title = {Extreme points of the unit ball of an operator space},
author = {Masayoshi Kaneda},
journal= {arXiv preprint arXiv:math/0408235},
year = {2009}
}
Comments
27 pages, http://www.math.uci.edu/~mkaneda/