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Let T be a contraction acting on the Hilbert space H such thatlimn||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||T*nh||0 holds for every nonzeroh H, then T is shown to be reflexive. 相似文献
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