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http://dx.doi.org/10.4134/JKMS.2003.40.6.933

PARANORMAL CONTRACTIONS AND INVARIANT SUBSPACES  

Duggal, B.P. (United Arab Emirates University)
Kubrusly, C.S. (Catholic University of Rio de Janeiro)
Levan, N. (University of California in Los Angeles)
Publication Information
Journal of the Korean Mathematical Society / v.40, no.6, 2003 , pp. 933-942 More about this Journal
Abstract
It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T/sup 2*/T/sup 2/ - 2T/sup */T ＋ I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contraction. Furthermore, if one of Q or D is compact, then so is the other, and Q and D are strict ontraction.
Keywords
paranormal operators; invariant subspaces; proper contractions;
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  • Reference
1 /
[ C.S.Kubrusly ] / An Introduction to Models and Decompositions in Operator Theory
2 Orbits of hyponormal operators /
[ P.S.Bourdon ] / Michigan Math. J.   DOI
3 Paranormal operators on Banach spaces /
[ N.N.Chourasia;P.B.Ramanujan ] / Bull. Austral. Math. Soc.   DOI
4 The unitary part of paranormal operators /
[ K.Okubo ] / Hokkaido Math. J.   DOI
5 /
[ B. Sz.-Nagy;C.Foias ] / Harmonic Analysis of Operators on Hilbert Space
6 /
[ B.P.Duggal;I.H.Jeon;C.S.Kubrusly ] / Contractions satisfying the absolute value property |A|² ≤ |A²|
7 On characterising contractions with <TEX>$C_{10}$</TEX> pure part /
[ B.P.Duggal ] / Integral Equations Operator Theory   DOI
8 Roots of contractions with Hilbert-Schmidt defect operator and <TEX>$C._{0}$</TEX> completely non-unitary part /
[ B.P.Duggal ] / Comment. Math., Ann. Soc. Math. Polonae
9 Proper contractions and invariant subspaces /
[ C.S.Kubrusly;N.Levan ] / Internat. J. Math. Math. Sci.   DOI   ScienceOn
10 Strong stability for cohyponormal operators /
[ C.S.Kubrusly;P.C.M.Vieira ] / J. Operator Theory
11 Paranormal operators with countable spectrum are normal operators /
[ C.Qiu ] / J. Math. Res. Exposition
12 Hyponormal operators and related topics /
[ T.Saito ] / Lectures on Operator Algebras, Lecture Notes in Math.
13 The Theory of Subnormal Operators, Mathematical Surveys and Monographs /
[ J.B.Conway ] / Amer. Math. Soc.,Providence
14 A decomposition for a class of contractions /
[ C.S.Kubrusly;P.C.M.Vieira;D.O.Pinto ] / Adv. Math. Sci. Appl.
15 Operators with a norm condition /
[ T.Ando ] / Acta Sci. Math. (Szeged)
16 /
[ H.Radjavi;P.Rosenthal ] / Invariant Subspaces