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April 1999 The unitary part of class $\mathcal {F}$ contractions
Takashi Yoshino
Proc. Japan Acad. Ser. A Math. Sci. 75(4): 50-52 (April 1999). DOI: 10.3792/pjaa.75.50


We say that a bounded linear operator $T$ on a Hilbert space $\mathcal{H}$ belongs to the class $\mathcal{F}$ if $T$ satisfies the following Fuglede's property that, for a given isometry $W$ on $\mathcal{H}$, $SW^*=TS$ for some bounded linear operator $S$ on $\mathcal{H}$ always implies $SW=T^*S$. Such class is wider than the class of paranormal contractions, the class of dominant operators and the class $\mathcal{Y}$ which was introduced in [4]. In this paper, we prove that, for the class $\mathcal{F}$ contraction $T$ on $\mathcal{H}$, the positive square root $A_{T^*}$ of the strong limit of $T^nT^{*n}$ is the projection from $\mathcal{H}$ onto $\mathcal{H}_T^{(u)}$ on which the unitary part of $T$ acts.


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Takashi Yoshino. "The unitary part of class $\mathcal {F}$ contractions." Proc. Japan Acad. Ser. A Math. Sci. 75 (4) 50 - 52, April 1999.


Published: April 1999
First available in Project Euclid: 23 May 2006

zbMATH: 0939.47017
MathSciNet: MR1701524
Digital Object Identifier: 10.3792/pjaa.75.50

Primary: 47A65 , 47B20

Keywords: contraction , dominant operators , hyponormal operators , paranormal operators , unitary part

Rights: Copyright © 1999 The Japan Academy


Vol.75 • No. 4 • April 1999
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