Ebook: 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.

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Content:
Front Matter....Pages i-xvii
Approximation Properties of Nuclear Frechet Spaces....Pages 1-10
Topics on Projective Spectra of (LB)-Spaces....Pages 11-27
Applications of the Projective Limit Functor to Convolution and Partial Differential Equations....Pages 29-46
Partial Differential Operators with Continuous Linear Right Inverse....Pages 47-62
Hartogs Type Extension Theorem of Real Analytic Solutions of Linear Partial Differential Equations with Constant Coefficients....Pages 63-72
Remarks on the Existence of Solutions of Partial Differential Equations in Gevrey Spaces....Pages 73-78
Tame Right Inverses for Partial Differential Equations....Pages 79-114
Stein Spaces M for which O(M) is Isomorphic to a Power Series Space....Pages 115-154
Monomial Expansions in Infinite Dimensional Holomorphy....Pages 155-171
Relations between ?0 and ?? on Spaces of Holomorphic Functions....Pages 173-180
Some Recent Results on VC(X)....Pages 181-194
Projective Descriptions of Weighted Inductive Limits: The Vector-Valued Cases....Pages 195-221
On Tensor Product ?-Algebra Bundles....Pages 223-233
Quojection and Prequojections....Pages 235-254
Nuclear K?the Quotients of Frechet Spaces....Pages 255-258
A Note on Strict LF-Spaces....Pages 259-264
Automatic Continuity in Frechet Algebras....Pages 265-268
Some Special K?the Spaces....Pages 269-296
On Pelczynski’s Problem....Pages 297-304
Some Invariants of Frechet Spaces and Imbeddings of Smooth Sequence Spaces....Pages 305-324
On Complemented Subspaces of Certain Nuclear K?the Spaces....Pages 325-332
Some New Methods in the Structure Theory of Nuclear Fr?chet Spaces....Pages 333-353
Every Quojection is the Quotient of a Countable Product of Banach Spaces....Pages 355-356
Dual K?mura Spaces....Pages 357-363

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Content:
Front Matter....Pages i-xvii
Approximation Properties of Nuclear Frechet Spaces....Pages 1-10
Topics on Projective Spectra of (LB)-Spaces....Pages 11-27
Applications of the Projective Limit Functor to Convolution and Partial Differential Equations....Pages 29-46
Partial Differential Operators with Continuous Linear Right Inverse....Pages 47-62
Hartogs Type Extension Theorem of Real Analytic Solutions of Linear Partial Differential Equations with Constant Coefficients....Pages 63-72
Remarks on the Existence of Solutions of Partial Differential Equations in Gevrey Spaces....Pages 73-78
Tame Right Inverses for Partial Differential Equations....Pages 79-114
Stein Spaces M for which O(M) is Isomorphic to a Power Series Space....Pages 115-154
Monomial Expansions in Infinite Dimensional Holomorphy....Pages 155-171
Relations between ?0 and ?? on Spaces of Holomorphic Functions....Pages 173-180
Some Recent Results on VC(X)....Pages 181-194
Projective Descriptions of Weighted Inductive Limits: The Vector-Valued Cases....Pages 195-221
On Tensor Product ?-Algebra Bundles....Pages 223-233
Quojection and Prequojections....Pages 235-254
Nuclear K?the Quotients of Frechet Spaces....Pages 255-258
A Note on Strict LF-Spaces....Pages 259-264
Automatic Continuity in Frechet Algebras....Pages 265-268
Some Special K?the Spaces....Pages 269-296
On Pelczynski’s Problem....Pages 297-304
Some Invariants of Frechet Spaces and Imbeddings of Smooth Sequence Spaces....Pages 305-324
On Complemented Subspaces of Certain Nuclear K?the Spaces....Pages 325-332
Some New Methods in the Structure Theory of Nuclear Fr?chet Spaces....Pages 333-353
Every Quojection is the Quotient of a Countable Product of Banach Spaces....Pages 355-356
Dual K?mura Spaces....Pages 357-363
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