Kérchy László honlapja

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Cím:On homogeneous contractions.
Szerző:K\'erchy, L\'aszl\'o
Forrás:J. Oper. Theory 41, No.1, 121-126 (1999).
Absztrakt:Summary: It was proved by {\it B. Bagchi} and {\it G. Misra} [J. Oper. Theory 37, No. 1, 51-65 (1997; Zbl 0871.47008)] that if $T$ is a homogeneous contraction such that the restriction $T|{\Cal D}_T$ of $T$ to the defect space ${\Cal D}_T$ is of Hilbert-Schmidt class, then $T$ has a constant characteristic function. We show that the assumption on $T|{\Cal D}_T$ can be relaxed assuming only the compactness of $T|{\Cal D}_T$. In fact, it turns out that the proof relies solely on the special ``decreasing" structure of the spectrum of the absolute value of $T|{\Cal D}_T$. 
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