A note on the differences of the consecutive powers of operators

Święch, Andrzej. "A note on the differences of the consecutive powers of operators." Banach Center Publications 38.1 (1997): 381-383. <http://eudml.org/doc/208642>.

@article{Święch1997,
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.},
author = {Święch, Andrzej},
journal = {Banach Center Publications},
keywords = {precompact; operator norm; spectrum; power bounded},
language = {eng},
number = {1},
pages = {381-383},
title = {A note on the differences of the consecutive powers of operators},
url = {http://eudml.org/doc/208642},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Święch, Andrzej
TI - A note on the differences of the consecutive powers of operators
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 381
EP - 383
AB - 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.
LA - eng
KW - precompact; operator norm; spectrum; power bounded
UR - http://eudml.org/doc/208642
ER -