# Journal of Operator Theory

Volume 90, Issue 1, Summer 2023 pp. 191-208.

Bounded point evaluation for operators with the
wandering subspace property

**Authors**:
Shailesh Trivedi

**Author institution:** Department of Mathematics, Birla Institute of
Technology and Science, Pilani-333031, India

**Summary: ** We extend and study the notion of bounded point
evaluation introduced by Williams for a cyclic operator to the class of
operators with the wandering subspace property. We characterize the set
$\mathrm{bpe}(T)$ of all bounded point evaluations for an operator $T$ with
the wandering subspace property in terms of the invertibility of certain
projections. Further, we determine $\mathrm{bpe}(T)$ and $\mathrm{abpe}(T)$
for a left-invertible operator $T$ with the wandering subspace property.
We also give examples of left-invertible operators $T$ with the wandering
subspace property for which $\mathbb D (0, r(T')^{-1} ) \subsetneqq
\mathrm{abpe}(T) \subseteq \mathrm{bpe}(T)$, where $r(T')$ is the spectral
radius of the Cauchy dual $T'$ of $T$.

**DOI: **http://dx.doi.org/10.7900/jot.2021nov05.2354

**Keywords: ** Bounded point evaluation, wandering subspace property,
weighted\break shift, directed graph.

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