This is the abstract of the paper
  "Elliptic Operators with Infinite-Dimensional State Spaces"
by Herbert Amann.

For the whole paper send the command

  get evolve-l 01-00007

to: "listserv@uni-karlsruhe.de".

Instead you may get the paper at
  "http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html"
too.

Abstract:
Motivated by applications to problems from physics, we study elliptic
operators
with operator-valued coefficients acting on Banach-space-valued
distributions.
After giving a definition of ellipticity, normal ellipticity in
particular,
generalizing the classical concepts, we show that normally elliptic
operators
are negative generators of analytic semigroups on $L_p(\mathbb R^n,E)$ for
$1\leq p<\infty$, and on $BUC(\mathbb R^n,E)$
and $C_0(\mathbb R^n,E)$, as well as on all Besov spaces of
$E$-valued distributions on $\mathbb R^n$, where $E$ is any Banach space.
This is true under minimal regularity assumptions for the coefficients,
thanks to a point-wise multiplier theorem for $E$-valued distributions proven
in the appendix.

Journal of Evolution Equations (JEE), {\bf1}(2001), ...

------------------  http://www.uni-karlsruhe.de/~listserv/  -------------------