CONTRACTIONS OF CLASS Q AND INVARIANT SUBSPACES
CONTRACTIONS OF CLASS Q AND INVARIANT SUBSPACES
A Hilbert Space operator T is of class Q if <TEX>$T^2{\ast}T^2-2T{\ast}T + I$</TEX> is nonnegative. Every paranormal operator is of class Q, but class-Q operators are not necessarily normaloid. It is shown that if a class-Q contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, …