TY - JOUR
AU - 전인호
DA - 2004
UR - http://dspace.ewha.ac.kr/handle/2015.oak/242754
AB - Let B (H) denote the algebra of operators on a complex Hilbert space H, and let u denote the class of operators A ∈ B(H) which satisfy the absolute value condition
AB - A
AB - 2 ≤
AB - A2
AB - . It is proved that if A ∈ u is a contraction, then either A has a nontrivial invariant subspace or A is a proper contraction and the nonnegative operator D =
AB - -
AB - 2 is strongly stable. A Putnam-Fuglede type commutativity theorem is proved for contractions A in U, and it is shown that if normal subspaces of A ∈ U are reducing, then every compact operator in the intersection of the weak closure of the range of the derivation δA(X) = AX - XA with the commutant of A* is quasinilpotent.
LA - English
TI - Contractions satisfying the absolute value property
TI - A
TI - 2 ≤
TI - A2
IS - 2
VL - 49
DO - 10.1007/s00020-002-1202-z
ER -