During the last two decades there has been a significant development
of many topics in differential analysis in infinite dimensional spaces.
New techniques, such as ultraproducts and ultrapowers, have thrown light
on the relationship between the geometric properties of Banach spaces
and the existence of differentiable functions on the spaces.
A special session on Differential Analysis on Infinite Dimensional
Spaces was held at the Summer meeting of the American Mathematical Society
at SUNY, Albany, N.Y., August 8- 11, 1983. The session consisted of
three meetings of three forty-minute talks each. This volume contains
the articles submitted by most of the participants in the special
session as well as articles by those who were invited but could not
be present at the meeting.
We thank all the participants and the contributors for their cooperation.
It is a pleasure to acknowledge our gratitude to the editorial committee
of the Contemporary Mathematics Series for including these proceedings
in the Series. Finally, we are thankful to the staff of the AMS for
their efficient service, help during the Session and cooperation.