Less than one implies zero

Felix L. Schwenninger, and Hans Zwart. "Less than one implies zero." Studia Mathematica 229.2 (2015): 181-188. <http://eudml.org/doc/285921>.

@article{FelixL2015,
abstract = {In this paper we show that from an estimate of the form $sup_\{t≥0\} ||C(t) - cos(at)I|| < 1$, we can conclude that C(t) equals cos(at)I. Here $(C(t))_\{t≥0\}$ is a strongly continuous cosine family on a Banach space.},
author = {Felix L. Schwenninger, Hans Zwart},
journal = {Studia Mathematica},
keywords = {cosine families; operator cosine functions; zero-one-law},
language = {eng},
number = {2},
pages = {181-188},
title = {Less than one implies zero},
url = {http://eudml.org/doc/285921},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Felix L. Schwenninger
AU - Hans Zwart
TI - Less than one implies zero
JO - Studia Mathematica
PY - 2015
VL - 229
IS - 2
SP - 181
EP - 188
AB - In this paper we show that from an estimate of the form $sup_{t≥0} ||C(t) - cos(at)I|| < 1$, we can conclude that C(t) equals cos(at)I. Here $(C(t))_{t≥0}$ is a strongly continuous cosine family on a Banach space.
LA - eng
KW - cosine families; operator cosine functions; zero-one-law
UR - http://eudml.org/doc/285921
ER -