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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Duality theory for covariant systems

Author: Magnus B. Landstad
Journal: Trans. Amer. Math. Soc. 248 (1979), 223-267
MSC: Primary 46L55
MathSciNet review: 522262
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Abstract: If $ (A,\rho ,G)$ is a covariant system over a locally compact group G, i.e. $ \rho $ is a homomorphism from G into the group of $ ^{\ast}$-automorphisms of an operator algebra A, there is a new operator algebra $ \mathfrak{A}$ called the covariance algebra associated with $ (A,\rho ,G)$. If A is a von Neumann algebra and $ \rho $ is $ \sigma $-weakly continuous, $ \mathfrak{A}$ is defined such that it is a von Neumann algebra. If A is a $ {C^{\ast}}$-algebra and $ \rho $ is norm-continuous $ \mathfrak{A}$ will be a $ {C^{\ast}}$-algebra. The following problems are studied in these two different settings: 1. If $ \mathfrak{A}$ is a covariance algebra, how do we recover A and $ \rho $? 2. When is an operator algebra $ \mathfrak{A}$ the covariance algebra for some covariant system over a given locally compact group G?

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Keywords: Operator algebra, covariant system, covariance algebra
Article copyright: © Copyright 1979 American Mathematical Society