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- W1586562419 abstract "Let $mu$ be a finite, positive Borel measure with support in ${z: |z| leq 1}$ such that $P^2(mu )$ â the closure of the polynomials in $L^2(mu )$ â is irreducible and each point in $mathbb {D} := {z: |z| < 1}$ is a bounded point evaluation for $P^2(mu )$. We show that if $mu (partial {mathbb {D}}) > 0$ and there is a nontrivial subarc $gamma$ of $partial {mathbb {D}}$ such that [ int _{gamma }log(mbox {small {$frac {dmu }{dm}$}})dm > -infty ,] then $dim (mathcal {M}ominus zmathcal {M}) = 1$ for each nontrivial closed invariant subspace $mathcal {M}$ for the shift $M_z$ on $P^2(mu )$." @default.
- W1586562419 created "2016-06-24" @default.
- W1586562419 creator A5002281947 @default.
- W1586562419 date "2002-04-11" @default.
- W1586562419 modified "2023-09-23" @default.
- W1586562419 title "A note concerning the index of the shift" @default.
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- W1586562419 doi "https://doi.org/10.1090/s0002-9939-02-06464-x" @default.
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