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 $T|{\Cal D}_T$. |