Advances in the Theory of Fréchet Spaces

Frechet spaces have been studied since the days of Banach. These spaces, their inductive limits and their duals played a prominent role in the development of the theory of locally convex spaces. Also they are natural tools in many areas of real and complex analysis. The pioneering work of Grothendieck in the fifties has been one of the important sources of inspiration for research in the theory of Frechet spaces. A structure theory of nuclear Frechet spaces emerged and some important questions posed by Grothendieck were settled in the seventies. In particular, subspaces and quotient spaces of stable nuclear power series spaces were completely characterized. In the last years it has become increasingly clear that the methods used in the structure theory of nuclear Frechet spaces actually provide new insight to linear problems in diverse branches of analysis and lead to solutions of some classical problems. The unifying theme at our Workshop was the recent developments in the theory of the projective limit functor. This is appropriate because of the important role this theory had in the recent research. The main results of the structure theory of nuclear Frechet spaces can be formulated and proved within the framework of this theory. A major area of application of the theory of the projective limit functor is to decide when a linear operator is surjective and, if it is, to determine whether it has a continuous right inverse.

Inhalt

Approximation properties of nuclear Fréchet spaces.- Topics on projective spectra of (LB)-spaces.- Applications of the projective limit functor to convolution and partial differential equations.- Partial differential operators with continuous linear right inverse.- Hartogs type extension theorem of real analytic solutions of linear partial differential equations with constant coefficients.- Remarks on the existence of solutions of partial differential equations in Gevrey spaces.- Tame right inverses for partial differential equations.- Stein spaces M for which O(M) is isomorphic to a power series space.- Monomial expansions in infinite dimensional holomorphy.- Relations between ?0 and ?? on spaces of holomorphic functions.- Some recent results on VC(X).- Projective descriptions of weighted inductive limits: The vector-valued cases.- On tensor product ?-algebra bundles.- Quojection and prequojections.- Nuclear Köthe quotients of Fréchet spaces.- A note on strict LF-spaces.- Automatic continuity in Fréchet algebras.- Some special Köthe spaces.- On Pelczynski's problem.- Some invariants of Fréchet spaces and imbeddings of smooth sequence spaces.- On complemented subspaces of certain nuclear Köthe spaces.- Some new methods in the structure theory of nuclear Fréchet spaces.- Every quojection is the quotient of a countable product of Banach spaces.- Dual K?mura spaces.