ABSTRACT
Let be the Banach algebra of all bounded linear operators on a complex Banach space X. Let XT({λ}) denote the local spectral subspace of an operator
associated with a singleton
, and fix a scalar
. We characterize maps ϕ on
which satisfy
Furthermore, we give a characterization of maps ϕ on
for which ϕ(0) = 0 and
AMS CLASSIFICATIONs:
Acknowledgments
The author wishes to express his thanks to the referee for his/her remarks and comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).