Invariant Subspaces of C1.-Contractions with Non-Reductive Unitary Extensions |
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Authors: | Kerchy L |
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Institution: | Bolyai Institute, University Szeged Aradi vértanuk tere 1, 6720 Szeged, Hungary |
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Abstract: | Let T be a contraction acting on the Hilbert space H such thatlimn![->](http://blms.oxfordjournals.org/math/rarr.gif) ||Tnh|| 0, for every nonzero h ;H. It is proved that if theunitary operator attached to T in a canonic way contains thebilateral shift, then T has a non-trivial invariant subspace.Furthermore, if in addition limn![->](http://blms.oxfordjournals.org/math/rarr.gif) ||T*nh|| 0 holds for every nonzeroh H, then T is shown to be reflexive. |
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