JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Dissertationes Mathematicae / Wszystkie zeszyty

## Dissertationes Mathematicae

Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po podpisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2009 są ogólnodostępne (bezpłatnie).

## Covariant representations for possibly singular actions on $C^*$-algebras

### Tom 549 / 2020

Dissertationes Mathematicae 549 (2020), 1-94 MSC: Primary 46L60; Secondary 46L55, 81T05, 46L40, 46L30. DOI: 10.4064/dm793-6-2019 Opublikowany online: 8 May 2020

#### Streszczenie

Singular actions on $C^*$-algebras are automorphic group actions on $C^*$-algebras, where the group is not locally compact, or the action is not strongly continuous. We study the covariant representation theory of actions which may be singular. In the usual case of strongly continuous actions of locally compact groups on $C^*$-algebras, this is done via crossed products, but this approach is not available for singular $C^*$-actions. We explored extension of crossed products to singular actions in a previous paper. The literature regarding covariant representations for possibly singular actions is already large and scattered, and in need of some consolidation. We collect in this survey a range of results in this field, mostly known. We improve some proofs and elucidate some interconnections. These include existence theorems by Borchers and Halpern, Arveson spectra, the Borchers–Arveson theorem, standard representations and Stinespring dilations as well as ground states, KMS states and ergodic states and the spatial structure of their GNS representations.

#### Autorzy

• Daniel BeltiţăInstitute of Mathematics “Simion Stoilow” of the Romanian Academy
P.O. Box 1-764
Bucureşti, Romania
e-mail
• Hendrik GrundlingDepartment of Mathematics
University of New South Wales
Sydney, NSW 2052, Australia
e-mail
• Karl-Hermann NeebDepartment of Mathematics
Friedrich-Alexander-Universität Erlangen-Nürnberg
Cauerstr. 11
91058 Erlangen, Germany
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek