Journal of Operator Theory

Volume 41, Issue 1, Winter 1999 pp. 121-126.

On homogeneous contractions

Authors: Laszlo Kerchy
Author institution: Bolyai Institute, University of Szeged, Arad vertanuk tere 1, H-6720 Szeged, Hungary

Summary: It was proved by B. Bagchi and G. Misra in [1] that if $T$ is a homogeneous contraction such that the restriction $T|\d_T$ of $T$ to the defect space $\d_T$ is of Hilbert-Schmidt class, then $T$ has a constant characteristic function. We show that the assumption on $T|\d_T$ can be relaxed assuming only the compactness of $T|\d_T$. In fact, it turns out that the proof relies solely on the special ``decreasing" structure of the spectrum of the absolute value of $T|\d_T$.

Keywords: Contraction, homogeneous operator, characteristic function, Mobius transformation

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