Crossed Products of 𝐶*-Algebras

Williams, Dana P.

doi:10.1090/surv/134

Cited by 362 publications

(685 citation statements)

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“…Rie↵el [Rie04, Section 1] handles continuous bounded functions to a C ⇤ -algebra using C ⇤ -valued weights. [Wil07] can be applied to the positive and negative variations of the real and imaginary parts of a complex measure. We prefer to use [Wil07] as our reference for vector-valued integration, mainly because it entails absolute integrability rather than unconditional integrability (see the first item in the following list).…”

Section: ⇤ -Ramificationsmentioning

confidence: 99%

Operator Algebras and Their Applications

Doran

Park

2016

Contemporary Mathematics

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Abstract. Three properness conditions for actions of locally compact groups on C ⇤ -algebras are studied, as well as their dual analogues for coactions. To motivate the properness conditions for actions, the commutative cases (actions on spaces) are surveyed; here the conditions are known: proper, locally proper, and pointwise properness, although the latter property has not been so well studied in the literature. The basic theory of these properness conditions is summarized, with somewhat more attention paid to pointwise properness. C ⇤ -characterizations of the properties are proved, and applications to C ⇤ -dynamical systems are examined. This paper is partially expository, but some of the results are believed to be new.

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Section: ⇤ -Ramificationsmentioning

confidence: 99%

Operator Algebras and Their Applications

Doran

Park

2016

Contemporary Mathematics

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“…The aim of this section is to establish the following p-version of the Stonevon Neumann Theorem ( [22,Theorem 4.23]). We let D = {M a : a ∈ C 0 (G)}.…”

Section: A P-version Of the Stone-von Neumann Theoremmentioning

confidence: 99%

Sets of p-multiplicity in locally compact groups

Todorov

Turowska

2015

Studia Math.

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Abstract. We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if the set E * = {(s, t) : ts −1 ∈ E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a pversion of the Stone-von Neumann Theorem.

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“…The topological structure of Homeo(Ω) can be described by the following lemma, the proof of which is given by [12 Lemma 6.1. The strong operator topology on Homeo(Ω) equals the topology with as subbasis elements of the form…”

Section: Positive Representations Inmentioning

confidence: 99%

Compact groups of positive operators on Banach lattices

Jeu

Wortel

2014

Indagationes Mathematicae

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Abstract. In this paper we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is compact in the strong operator topology, it equals a group of isometric positive operators conjugated by a single central lattice automorphism, provided an additional technical assumption is satisfied, for which we have only examples. We obtain a characterization of positive representations of a group with compact image in the strong operator topology, and use this for normalized symmetric Banach sequence spaces to prove an ordered version of the decomposition theorem for unitary representations of compact groups. Applications concerning spaces of continuous functions are also considered.

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Crossed Products of 𝐶*-Algebras

Cited by 362 publications

References 0 publications

Operator Algebras and Their Applications

Operator Algebras and Their Applications

Sets of p-multiplicity in locally compact groups

Compact groups of positive operators on Banach lattices

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