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Kaplansky’s theorem
and Banach PI-algebras
Vladimír Müller |
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Vol. 141 (1990), No. 2, 355–361
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Abstract |
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By the theorem of Kaplansky a bounded operator in a Banach space is algebraic if and only if it is locally algebraic. We prove a generalization of this theorem. As a corollary we obtain the analogous result for finite (or countable) families of operators. Further we prove that a Banach algebra is PI (i.e. it satisfies a polynomial identity) if and only if it is locally PI. |
Mathematical Subject Classification 2000
Primary: 46H05
Secondary: 47A99
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Milestones
Received: 23 March 1988
Published: 1 February 1990
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Authors |
| Vladimír Müller | |
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