Geodesic
Connectedness of the Invertibles in Certain Nest Algebras
Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 412-420

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DOI

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.
DOI : 10.4153/CMB-1995-060-6
Mots-clés : 47D25 
Davidson, Kenneth R.; Lindsay, John; Pitts, David R. Connectedness of the Invertibles in Certain Nest Algebras. Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 412-420. doi: 10.4153/CMB-1995-060-6
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     author = {Davidson, Kenneth R. and Lindsay, John and Pitts, David R.},
     title = {Connectedness of the {Invertibles} in {Certain} {Nest} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {412--420},
     year = {1995},
     volume = {38},
     number = {4},
     doi = {10.4153/CMB-1995-060-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-060-6/}
}
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