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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on the connectedness problem for nest algebras


Author: David R. Pitts
Journal: Proc. Amer. Math. Soc. 114 (1992), 181-183
MSC: Primary 47D25; Secondary 47B38, 47D03, 47D30
DOI: https://doi.org/10.1090/S0002-9939-1992-1062833-6
MathSciNet review: 1062833
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Abstract: It has been conjectured that a certain operator $ T$ belonging to the group $ \mathcal{G}$ of invertible elements of the algebra $ \operatorname{Alg} {\mathbf{Z}}$ of doubly infinite upper-triangular bounded matrices lies outside the connected component of the identity in $ \mathcal{G}$. In this note we show that $ T$ actually lies inside the connected component of the identity of $ \mathcal{G}$.


References [Enhancements On Off] (What's this?)

  • [1] Kenneth R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1988. Triangular forms for operator algebras on Hilbert space. MR 972978
  • [2] Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York, Toronto, London, 1952. MR 0045823

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1062833-6
Keywords: Nest, nest algebra
Article copyright: © Copyright 1992 American Mathematical Society