Eventually positive elements in ordered Banach algebras
Gerd Herzog; Peer C. Kunstmann
Commentationes Mathematicae Universitatis Carolinae (2023)
- Volume: 64, Issue: 3, page 321-330
- ISSN: 0010-2628
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topHerzog, Gerd, and Kunstmann, Peer C.. "Eventually positive elements in ordered Banach algebras." Commentationes Mathematicae Universitatis Carolinae 64.3 (2023): 321-330. <http://eudml.org/doc/299212>.
@article{Herzog2023,
abstract = {In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since our structural assumptions on the ordered Banach algebra are much weaker.},
author = {Herzog, Gerd, Kunstmann, Peer C.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ordered Banach algebra; eventually positive element; spectral property; Perron--Frobenius property},
language = {eng},
number = {3},
pages = {321-330},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Eventually positive elements in ordered Banach algebras},
url = {http://eudml.org/doc/299212},
volume = {64},
year = {2023},
}
TY - JOUR
AU - Herzog, Gerd
AU - Kunstmann, Peer C.
TI - Eventually positive elements in ordered Banach algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 3
SP - 321
EP - 330
AB - In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since our structural assumptions on the ordered Banach algebra are much weaker.
LA - eng
KW - ordered Banach algebra; eventually positive element; spectral property; Perron--Frobenius property
UR - http://eudml.org/doc/299212
ER -
References
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