Kreiss bounded and uniformly Kreiss bounded operators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542394" target="_blank" >RIV/67985840:_____/21:00542394 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13163-020-00355-x" target="_blank" >https://doi.org/10.1007/s13163-020-00355-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13163-020-00355-x" target="_blank" >10.1007/s13163-020-00355-x</a>
Alternative languages
Result language
angličtina
Original language name
Kreiss bounded and uniformly Kreiss bounded operators
Original language description
If T is a Kreiss bounded operator on a Banach space, then ‖ Tn‖ = O(n). Forty years ago Shields conjectured that in Hilbert spaces, ‖Tn‖=O(n). A negative answer to this conjecture was given by Spijker, Tracogna and Welfert in 2003. We improve their result and show that this conjecture is not true even for uniformly Kreiss bounded operators. More precisely, for every ε> 0 there exists a uniformly Kreiss bounded operator T on a Hilbert space such that ‖ Tn‖ ∼ (n+ 1) 1 - ε for all n∈ N. On the other hand, any Kreiss bounded operator on Hilbert spaces satisfies ‖Tn‖=O(nlogn). We also prove that the residual spectrum of a Kreiss bounded operator on a reflexive Banach space is contained in the open unit disc, extending known results for power bounded operators. As a consequence we obtain examples of mean ergodic Hilbert space operators which are not Kreiss bounded.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista Mathématica Complutense
ISSN
1139-1138
e-ISSN
1988-2807
Volume of the periodical
34
Issue of the periodical within the volume
2
Country of publishing house
ES - SPAIN
Number of pages
19
Pages from-to
469-487
UT code for WoS article
000525361000001
EID of the result in the Scopus database
2-s2.0-85083390879