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Dilations for Polynomially Bounded Operators
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Abstract
We discuss a certain geometric property $X_{\theta, \gamma}$ of dual algebras generated by a polynomially bounded operator and property $({\A}_{\aleph_0,\aleph_0})$; these are central to the study of $\aleph_0 \times \aleph_0$-systems of simultaneous equations of weak*-continuous linear functionals on a dual algebra. In particular, we prove that if $T \in {\A}^M$ satisfies a certain sequential property, then $T \in \A^M_{\aleph_0}({\mathcal H}) $ if and only if the algebra ${\mathcal A}_T$ has property $X_{0, 1/M}$, which is an improvement of Li-Pearcy theorem in \cite{LP2}.
참고문헌 (9)
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- "A polynomially bounded operator onHilbert space which is not similar to a contraction", 10, pp.351~ (1997)
- "Harmonic analysis ofoperators on Hilbert space" (1970), North Holland Akademiai Kiado
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