On continuous Peirce decompositions, Schur multipliers and the perturbation of triple functional calculus
Every odd continuous function f on the real line
induces by a functional calculus on every
JB*-triple E (= hermitian Banach Jordan
triple system) a continuous map fE from E into
itself. The vector map fE may not be differentiable
even if the scalar function f has continuous derivatives.
We introduce for every element a in E a Peirce spectrum
(= a certain compact subset of the real plane) and show
for a big class of scalar functions f that the derivative
of fE in a exists and is a Schur multiplier with respect
to this spectrum.
J. Arazy
<jarazy@mathcs2.haifa.ac.il>
W. Kaup
<kaup@uni-tuebingen.de >