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Connectedness of the Invertibles in Certain Nest Algebras

Published online by Cambridge University Press:  20 November 2018

Kenneth R. Davidson ,
John Lindsay  and
David R. Pitts
Kenneth R. Davidson
Affiliation:
Pure Mathematics Department, University of Waterloo, Waterloo, Ontario, N2L 3G1, e-mail:krdavids@math.uwaterloo.ca
John Lindsay
Affiliation:
Mathematics Department, University of Nebraska, Lincoln, Nebraska 68588-0323, U.S.A. e-mail:jorr@unlinfo.uni.edu
David R. Pitts
Affiliation:
Mathematics Department, University of Nebraska, Lincoln, Nebraska 68588-0323, U.S.A. e-mail:dpitts@unlinfo2.unl.edu
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Abstract

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We show that if is a nest with no isolated atoms of finite multiplicity, then the invertibles in are connected. The key technical ingredient is that in such nest algebras, every operator with zero atomic diagonal part factors through the non-atomic part of . In particular, these results apply for the Cantor nest.

Keywords

47D25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995 , pp. 412 - 420
Copyright
Copyright © Canadian Mathematical Society 1995

References

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