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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the connectedness problem for nest algebras
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by David R. Pitts PDF
Proc. Amer. Math. Soc. 114 (1992), 181-183 Request permission

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
  • 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
  • Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1952. MR 0045823
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • 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