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2012, Volume 19: 49-57. Doi: 10.3934/era.2012.19.49

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Operator representations of logmodular algebras which admit $\gamma-$spectral $\rho-$dilations

1.
Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei No.2, Et. 2, 300006, Timişoara

Received: July 2011

Revised: April 2012

Published: January 2012

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Abstract

This paper deals with some semi-spectral representations of logmodular algebras. More exactly, we characterize such representations by the corresponding scalar semi-spectral measures. In the case of a logmodular algebra we obtain, for $0<\rho \leq 1,$ several results which generalize the corresponding results of Foiaş-Suciu [2] in the case $\rho =1.$

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Mathematics Subject Classification: Primary: 46J25, 47A20; Secondary: 46J10.

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References

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