Similarity of parts to the whole for certain multiplication operators

Author:
Paul S. Bourdon

Journal:
Proc. Amer. Math. Soc. **99** (1987), 563-567

MSC:
Primary 47B38; Secondary 47B35

MathSciNet review:
875398

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Abstract: We show that the Bergman shift , multiplication by on the Bergman space , is similar to its part if and only if , where is a finite product of interpolating Blaschke products. In addition, we show that is not unitarily equivalent to any of its parts. For the analytic Toeplitz operator on , we obtain that is similar to each of its parts if and only if is unitarily equivalent to each of its parts if and only if is a weak-star generator of .

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0875398-4

Article copyright:
© Copyright 1987
American Mathematical Society