Reflexivity of the commutant and local commutants of an algebraic operator |
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Authors: | Janko Bra?i? |
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Institution: | University of Ljubljana, IMFM, Jadranska ul. 19, SI-1000 Ljubljana, Slovenia |
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Abstract: | We show that an algebraic operator on a complex Banach space has reflexive commutant if and only if each zero of the minimal polynomial of the operator is simple. Further, for any operator, the local commutant at an eigenvector is reflexive. On the other hand, for an algebraic operator whose minimal polynomial has at least one zero that is not simple, the local commutant of the operator at a given vector is reflexive precisely when the vector is an eigenvector. |
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Keywords: | Primary 47L05 47B99 |
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