Author's: Haïkel Skhiri
Pages: [97] - [114]
Received Date: September 4, 2010
Submitted by:
Let be a complex unital Banach algebra and let
be the set of all algebra-norms on
equivalent to the given algebra-norm. In
this paper, we introduce the concept of
and
functions depending on a norm
and related to the notion of
“topological divisors of zeroâ€. We prove that some usual
measures of either non-compactness or non-strict-singularity of
operators, as well other quantities are
or
function. We prove several spectral radius
formulae for
and
functions. In particular, we prove that if
is a
or
function and
then
and
where denotes the spectral radius of x.
Banach algebra, left (resp., right) topological divisor of zero,
Calkin algebra, Fredholm operators, spectrum, spectral radius,
measures of noncompactness,