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Contractions satisfying the absolute value property

Title
Contractions satisfying the absolute value property; A

Title
A; 2 ≤

Title
2 ≤; A2

Title
A2
Authors
Duggal B.P.Jeon I.H.Kubrusly C.S.
Ewha Authors
전인호
Issue Date
2004
Journal Title
Integral Equations and Operator Theory
ISSN
0378-620XJCR Link
Citation
vol. 49, no. 2, pp. 141 - 148
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
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

A

2 ≤

A2

. 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 =

-

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.
DOI
10.1007/s00020-002-1202-z
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연구기관 > 수리과학연구소 > Journal papers
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