Compact operators without extended eigenvalues |
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| Authors: | S Shkarin |
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| Affiliation: | King's College London, Department of Mathematics, Strand, London WC2R 2LS, UK |
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| Abstract: | A complex number λ is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT=λTX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}. |
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| Keywords: | Extended eigenvalues Compact operators Quasinilpotent operators Similarity |
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