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Factorization of Positive Invertible Operators in af Algebras

Published online by Cambridge University Press:  20 November 2018

Houben Huang  and
Timothy D. Hudson
Houben Huang
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L 3G1
Timothy D. Hudson
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L 3G1
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Abstract

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We examine the problem of factoring a positive invertible operator in an AF C*-algebra as T*T for some invertible operator T with both T and T-1 in a triangular AF subalgebra. A factorization theorem for a certain class of positive invertible operators in AF algebras is proven. However, we explicitly construct a positive invertible operator in the CAR algebra which cannot be factored with respect to the 2∞ refinement algebra. Our main result generalizes this example, showing that in any AF algebra, there exist positive invertible operators which fail to factor with respect to a given triangular AF subalgebra. We also show that in the context of AF algebras, the notions of having a factorization and having a weak factorization are the same.

Keywords

46L0547D25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 2 , 01 April 1995 , pp. 421 - 435
Copyright
Copyright © Canadian Mathematical Society 1995

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