A note on the differences of the consecutive powers of operators
Volume 38 / 1997
Banach Center Publications 38 (1997), 381-383
DOI: 10.4064/-38-1-381-383
Abstract
We present two examples. One of an operator T such that ${T^n(T-I)}_{n=1}^∞$ is precompact in the operator norm and the spectrum of T on the unit circle consists of an infinite number of points accumulating at 1, and the other of an operator T such that ${T^n(T-I)}_{n=1}^∞$ is convergent to zero but T is not power bounded.
