Open projections in operator algebras I: Comparison theory

Details Open projections in operator algebras I: Comparison theory Open projections in operator algebras I: Comparison theory

2011-09-23

arxiv.org/abs/1109.5171v2

Mathematics

Operator Algebras

28 pages, To appear Studia Mathematica

Scientific paper

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.

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