Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] K. R. Davidson, Nest Algebras, Research Notes in Math., vol. 191, Pitman, Boston, London, and Melbourne, 1988. MR 972978 (90f:47062)
  • [2] Z. Nehari, Conformal mapping, 1st ed., Internat. Ser. Pure and Appl. Math., McGraw-Hill, New York, Toronto, and London, 1952. MR 0045823 (13:640h)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D25, 47B38, 47D03, 47D30

Retrieve articles in all journals with MSC: 47D25, 47B38, 47D03, 47D30


Additional Information

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

American Mathematical Society