𝑛th roots of operators
Mary R. Embry · Proceedings of the American Mathematical Society · 1968
I. Introduction.Let A and E be continuous linear transformations which map a Banach space into itself.If E commutes with An, for some integer n greater than 1, we do not necessarily know whether E commutes with A. The main purpose of this paper is to exhibit a proof of the following theorem:Let A and E be continuous linear trans/ormations which map a complex Banach space into itself.Let n be an integer greater than 1. 1/ a(A) r\a(e2rikl,,A) = 0 /or k = l, • • • , w-1 and E commutes with A", then E commutes with A.