Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DILATIONS FOR POLYNOMIALLY BOUNDED OPERATORS

  • EXNER, GEORGE R. (Department of Mathematics, Bucknell University) ;
  • JO, YOUNG SOO (Department of Mathematics, College of Natural Sciences) ;
  • JUNG, IL BONG (Department of Mathematics, College of Natural University)
  • Published : 2005.09.01
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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 ($\mathbb{A}_{N_0,N_0}$; these are central to the study of $N_{0}\timesN_{0}$-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}_{N_0}(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].

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References

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