DILATIONS FOR POLYNOMIALLY BOUNDED OPERATORS

EXNER, GEORGE R.; JO, YOUNG SOO; JUNG, IL BONG

doi:10.4134/JKMS.2005.42.5.893

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DILATIONS FOR POLYNOMIALLY BOUNDED OPERATORS

Journal title : Journal of the Korean Mathematical Society
Volume 42, Issue 5, 2005, pp.893-912
Publisher : The Korean Mathematical Society
DOI : 10.4134/JKMS.2005.42.5.893

Title & Authors

DILATIONS FOR POLYNOMIALLY BOUNDED OPERATORS
EXNER, GEORGE R.; JO, YOUNG SOO; JUNG, IL BONG;

Abstract

We discuss a certain geometric property X ${$\_{}$ of dual algebras generated by a polynomially bounded operator and property ( ${$\mathbb{A}$}$ , ${$\aleph$}$ , = ${$\aleph$}$ ) 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$}$ ${$\mathbb{A}$}$ ${$^{M}$}$ satisfies a certain sequential property, then T ${$\in$}$ ${$\mathbb{A}$}$ ${$^{M}$}$ ${$\_{}$ (H) if and only if the algebra A ${$\_{T}$}$ has property X ${$\_{0, 1/M}$}$ , which is an improvement of Li-Pearcy theorem in [8].

Keywords

polynomially bounded operator;dual operator algebra.;

Language

English

Cited by

References

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