# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Open projections in operator algebras I: Comparison theory

### Tom 208 / 2012

Studia Mathematica 208 (2012), 117-150 MSC: Primary 46L85, 46H10, 46L07, 47L30, 46H30; Secondary 06F25, 17C65, 46L08, 47L07. DOI: 10.4064/sm208-2-2

#### Streszczenie

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, Rørdam, 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.

#### Autorzy

• David P. BlecherDepartment of Mathematics
University of Houston
Houston, TX 77204-3008, U.S.A.
e-mail
• Matthew NealDepartment of Mathematics
Denison University
Granville, OH 43023, U.S.A.
e-mail

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