A note concerning the index of the shift

Author:
John R. Akeroyd

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3349-3354

MSC (2000):
Primary 47A53, 47B20, 47B38; Secondary 30E10, 46E15

Published electronically:
April 11, 2002

MathSciNet review:
1913014

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Abstract: Let be a finite, positive Borel measure with support in such that - the closure of the polynomials in - is irreducible and each point in is a bounded point evaluation for . We show that if and there is a nontrivial subarc of such that

then for each nontrivial closed invariant subspace for the shift on .

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Additional Information

**John R. Akeroyd**

Affiliation:
Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701

Email:
jakeroyd@comp.uark.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06464-X

Received by editor(s):
April 17, 2001

Received by editor(s) in revised form:
June 19, 2001

Published electronically:
April 11, 2002

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2002
American Mathematical Society