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)



The numerical range of a weighted shift

Author: Quentin F. Stout
Journal: Proc. Amer. Math. Soc. 88 (1983), 495-502
MSC: Primary 47B37; Secondary 47A12
MathSciNet review: 699421
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $T$ be a weighted shift on a Hilbert space. We compute the numerical radius of $T$ when $T$ is finite, circular, Hilbert-Schmidt, periodic, or a finite perturbation of periodic. For several cases we also determine whether the numerical range is closed, completing the determination of the numerical range and answering a question of Ridge. An important step is the determination of the eigenvalues of a selfadjoint tri-diagonal matrix with zeroes on its diagonal. We give a simple formula for the eigenvalues when the matrix is finite dimensional or Hilbert-Schmidt.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B37, 47A12

Retrieve articles in all journals with MSC: 47B37, 47A12

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society