Contractions Satisfying the Absolute Value Property |
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Authors: | BP Duggal IH Jeon and CS Kubrusly |
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Institution: | (1) Department of Mathematics, United Arab Emirates University, 17551, Al Ain, Arab Emirates;(2) Department of Mathematics, Ewha Women s University, Seoul, 120-750, Korea;(3) Catholic University of Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, Brazil |
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Abstract: | Let B(H) denote the algebra of operators on a complex Hilbert
space H, and let U denote the class of operators
which satisfy
the absolute value condition
.
It is proved that if
is a
contraction, then either A has a nontrivial invariant subspace or A is a proper
contraction and the nonnegative operator
is strongly stable. A Putnam-Fuglede type commutativity theorem is proved for contractions A in
,
and it is shown that if normal subspaces of
. It is proved that if
are reducing, then every compact operator in the intersection of the weak closure of the range of the
derivation
with the commutant of A* is quasinilpotent. |
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Keywords: | Primary: 47B20 47B47 Secondary: 47A15 47A63 |
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