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The Failure of Approximate Inner Conjugacy for Standard Diagonals in Regular Limit Algebras

Published online by Cambridge University Press:  20 November 2018

Allan P. Donsig  and
S. C. Power
Allan P. Donsig
Affiliation:
Dept. of Mathematics & Statistics, Lancaster University Lancaster, U.K. LAI 4YF, e-mail: apdonsig@math. uwaterloo. ca, power@unix.lancs.ac.uk
S. C. Power
Affiliation:
Dept. of Mathematics & Statistics, Lancaster University Lancaster, U.K. LAI 4YF, e-mail: apdonsig@math. uwaterloo. ca, power@unix.lancs.ac.uk
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Abstract

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AF C*-algebras contain natural AF masas which, here, we call standard diagonals. Standard diagonals are unique, in the sense that two standard diagonals in an AF C*-algebra are conjugate by an approximately inner automorphism. We show that this uniqueness fails for non-selfadjoint AF operator algebras. Precisely, we construct two standard diagonals in a particular non-selfadjoint AF operator algebra which are not conjugate by an approximately inner automorphism of the non-selfadjoint algebra.

Keywords

47D2546K50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 420 - 428
Copyright
Copyright © Canadian Mathematical Society 1996

References

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