Electronic Journal of Differential Equations: 
Vol. 1995(1995), No. 13, pp 1--17.

Title: Dichotomy and $H^\infty$ Functional Calculi

Authors: R. deLaubenfels (Scientia Research Institute, Athens, OH, USA)
         Y. Latushkin (Univ. of Missouri, Columbia, MO, USA)

Abstract: Dichotomy for the abstract Cauchy problem with any 
densely defined closed operator on a Banach space is studied.
We give conditions under which an operator with an $H^\infty$
functional calculus has dichotomy. For the operators with 
imaginary axis contained in the resolvent set and with 
polynomial growth of the resolvent along the axis we prove
the existence of  dichotomy on subspaces and superspaces.
Applications to the dichotomy of operators on $L_p$-spaces 
are given. The principle of linearized instability for 
nonlinear equations is proved.

Submitted August 1, 1995. Published September 21, 1995.
Math Subject Classification: 47D05, 47A60.
Key Words: Abstract Cauchy problem; operator semigroups; 
           exponential dichotomy; functional calculi.