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Order theory and interpolation in operator algebras

100%

Blecher D., Read C.

Studia Mathematica

2014

tom 225

nr 1

61-95

In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator algebra and the C*-algebra it generates. In much of this it is not necessary that the algebra have an approximate identity. Many of our results apply immediately to function algebras, but we will not take the time to point these out, although most of these applications seem new.

Ideals and hereditary subalgebras in operator algebras

81%

Almus M., Blecher D., Read C.

Studia Mathematica

2012

tom 212

nr 1

65-93

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.

Ograniczanie wyników

2 Studia Mathematica

2 Blecher D.

2 Read C.

1 Almus M.

1 2014

1 2012

Wyniki wyszukiwania

Order theory and interpolation in operator algebras

Ideals and hereditary subalgebras in operator algebras