On a question of Davidson and Paulsen
An example of a polynomially bounded operator on Hilbert space not similar to a contraction was found by \textit{G. Pisier} [J. Am. Math. Soc. 10, No.~2, 351-369 (1997; Zbl 0869.47014)]. An operator-theoretic proof that certain CAR-valued Foguel-Hankel operators are polynomially bounded operators but not similar to contractions was given by \textit{K. Davidson} and \textit{V. Paulsen} [J. Reine Angew. Math. 487, 153-170 (1997; Zbl 0890.47013)]. They also asked for a characterization of operators in this family which are similar to contractions. A partial answer was given by \textit{V. Paulsen} and the reviewer [Indiana Univ. Math. J. 50, No.~4, 1509-1522 (2001; Zbl 1031.47019)]. A full solution is given in the present paper. Some related results concerning Schur multipliers (when restricted to Hankel matrices) are also obtained.
scientific article; zbMATH DE number 1797599