Lomonosov's theorem cannot be extended to chains of four operators |
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| Authors: | Vladimir G Troitsky |
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| Institution: | Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green St., Urbana, Illinois 61801 |
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| Abstract: | We show that the celebrated Lomonosov theorem cannot be improved by increasing the number of commuting operators. Specifically, we prove that if  is the operator without a non-trivial closed invariant subspace constructed by C. J. Read, then there are three operators  ,  and  (non-multiples of the identity) such that  commutes with  ,  commutes with  ,  commutes with  , and  is compact. It is also shown that the commutant of  contains only series of  . |
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| Keywords: | Invariant subspaces commutant |
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