C*-algebras nearly contained in a type I C*-algebra

Erik Christensen; Allan M.  Sinclair; Stuart A.  White; Roger R. Smith

doi:10.4153/CJM-2012-001-1

C-algebras nearly contained in a type I C-algebra

Erik Christensen, Allan M. Sinclair, Stuart A. White, Roger R. Smith

Department of Mathematical Sciences

Abstract

In this paper we consider near inclusions A ⊆₇ B of C ^* -algebras. We show that if B is a separable type I C ^* -algebra and A satisfies Kadison's similarity problem, then A is also type I. We then use this to obtain an embedding of A into B.

Translated title of the contribution	C-algebraer som er næsten indeholdt i en type I C-algebra
Original language	English
Journal	Canadian Journal of Mathematics
Volume	65
Pages (from-to)	52-65
Number of pages	14
ISSN	0008-414X
DOIs	https://doi.org/10.4153/CJM-2012-001-1
Publication status	Published - Feb 2013

Keywords

Faculty of Science

Access to Document

10.4153/CJM-2012-001-1

Cite this

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title = "C*-algebras nearly contained in a type I C*-algebra",

abstract = "In this paper we consider near inclusions A ⊆7 B of C * -algebras. We show that if B is a separable type I C * -algebra and A satisfies Kadison's similarity problem, then A is also type I. We then use this to obtain an embedding of A into B.",

keywords = "Faculty of Science, Matematik",

author = "Erik Christensen and Sinclair, {Allan M.} and White, {Stuart A.} and Smith, {Roger R.}",

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language = "English",

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journal = "Canadian Journal of Mathematics",

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T1 - C*-algebras nearly contained in a type I C*-algebra

AU - Christensen, Erik

AU - Sinclair, Allan M.

AU - White, Stuart A.

AU - Smith, Roger R.

PY - 2013/2

Y1 - 2013/2

N2 - In this paper we consider near inclusions A ⊆7 B of C * -algebras. We show that if B is a separable type I C * -algebra and A satisfies Kadison's similarity problem, then A is also type I. We then use this to obtain an embedding of A into B.

AB - In this paper we consider near inclusions A ⊆7 B of C * -algebras. We show that if B is a separable type I C * -algebra and A satisfies Kadison's similarity problem, then A is also type I. We then use this to obtain an embedding of A into B.

KW - Faculty of Science

KW - Matematik

U2 - 10.4153/CJM-2012-001-1

DO - 10.4153/CJM-2012-001-1

M3 - Journal article

SN - 0008-414X

VL - 65

SP - 52

EP - 65

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics