dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor
Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author
Munhoz Rodrigues, Hildebrando
dc.contributor.author
Solà-Morales Rubió, Joan de
dc.identifier
Munhoz, H.; Sola-morales, J. A note on the relationship between spectral radius and norms of bounded linear operators. "Matemática contemporânea", 2009, vol. 36, p. 131-137.
dc.identifier
https://hdl.handle.net/2117/20577
dc.description.abstract
Let
X
be a Banach space and
L
(
X
) be the Banach algebra of bounded
operators on
X
. In this note we prove that if we have a compact subset
K
of a commutative sub-algebra of
L
(
X
), and given
" >
0, then it is
possible to de ne a new norm in
X
, equivalent to its given norm, in
such a way that inside a neighborhood
U
"
of this compact set in the sub-
algebra, the norms of all the operators di er from their spectral radius
in less than
"
. If
X
is a Hilbert space then it is possible to de ne this
new norm as an Hilbertian norm.
dc.description.abstract
Postprint (published version)
dc.format
application/pdf
dc.relation
http://www.mc.sbm.org.br/edicoes/36/36_9.pdf
dc.rights
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights
Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject
Banach, Espais de
dc.title
A note on the relationship between spectral radius and norms of bounded linear operators
