be a Banach space and
) be the Banach algebra of bounded
. In this note we prove that if we have a compact subset
of a commutative sub-algebra of
), and given
0, then it is
possible to de ne a new norm in
, equivalent to its given norm, in
such a way that inside a neighborhood
of this compact set in the sub-
algebra, the norms of all the operators di er from their spectral radius
in less than
is a Hilbert space then it is possible to de ne this
new norm as an Hilbertian norm.
CitacióMunhoz, 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.