Open projections in operator algebras I: Comparison theory

• Autorzy: David P. Blecher , Matthew Neal
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L30: Abstract operator algebras on Hilbert spaces
• 46H10: Ideals and subalgebras
• 46L07: Operator spaces and completely bounded maps
• 46L08: C * -modules
• 46L85: Noncommutative topology
• 46H30: Functional calculus in topological algebras
• 47L07: Convex sets and cones of operators
• 17C65: Jordan structures on Banach spaces and algebras
• 06F25: Ordered rings, algebras, modules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 208
• Numer: 2
• Strony: 117-150

Daty

wydano

2012

Twórcy

autor

David P. Blecher

• Department of Mathematics, University of Houston, Houston, TX 77204-3008, U.S.A.

autor

Matthew Neal

• Department of Mathematics, Denison University, Granville, OH 43023, U.S.A.

Identyfikatory

DOI

10.4064/sm208-2-2