On spectral continuity of positive elements

S. Mouton. "On spectral continuity of positive elements." Studia Mathematica 174.1 (2006): 75-84. <http://eudml.org/doc/284436>.

@article{S2006,
abstract = {Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the above inequalities.},
author = {S. Mouton},
journal = {Studia Mathematica},
keywords = {ordered Banach algebra; positive element; spectrum},
language = {eng},
number = {1},
pages = {75-84},
title = {On spectral continuity of positive elements},
url = {http://eudml.org/doc/284436},
volume = {174},
year = {2006},
}

TY - JOUR
AU - S. Mouton
TI - On spectral continuity of positive elements
JO - Studia Mathematica
PY - 2006
VL - 174
IS - 1
SP - 75
EP - 84
AB - Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the above inequalities.
LA - eng
KW - ordered Banach algebra; positive element; spectrum
UR - http://eudml.org/doc/284436
ER -