Kaplansky's theorem and Banach PI-algebras

Vladimír Müller
1990 Pacific Journal of Mathematics  
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.
doi:10.2140/pjm.1990.141.355 fatcat:hfqgt5idh5fntcv4h43heidoci