Ideals and hereditary subalgebras in operator algebras

• Autorzy: Melahat Almus , David P. Blecher , Charles John Read
• Języki publikacji: EN

Abstrakty

EN

This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which are 'weakly compact'. We also give several examples answering natural questions that arise in such an investigation.

Kategorie tematyczne

• 46L52: Noncommutative function spaces
• 47L30: Abstract operator algebras on Hilbert spaces
• 46H10: Ideals and subalgebras
• 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation
• 46L07: Operator spaces and completely bounded maps
• 47L40: Limit algebras, subalgebras of C * -algebras
• 47L25: Operator spaces (= matricially normed spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 212
• Numer: 1
• Strony: 65-93

Daty

wydano

2012

Twórcy

autor

Melahat Almus

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

autor

David P. Blecher

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

autor

Charles John Read

• Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England

Identyfikatory

DOI

10.4064/sm212-1-5