Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor'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 zero”. 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,
