1109.5171 (David P. Blecher et al.)

Open projections in operator algebras I: Comparison theory    [PDF]

David P. Blecher, Matthew Neal

We begin a program of generalizing basic elements of the theory of
comparison, equivalence, and subequivalence, of elements in C*-algebras, to the
setting of more general algebras. In particular, we follow the recent lead of
Lin, Ortega, Rordam, and Thiel of studying these equivalences, etc., in terms
of open projections or module isomorphisms. We also define and characterize a
new class of inner ideals in operator algebras, and develop a matching theory
of open partial isometries in operator ideals which simultaneously generalize
the open projections in operator algebras (in the sense of the authors and
Hay), and the open partial isometries (tripotents) introduced by the authors.

View original: http://arxiv.org/abs/1109.5171