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We provide new characterizations of acyclic inductive spectra of Fréchet spaces which improve the classical theorem of Palamodov and Retakh. It turns out that acyclicity, sequential retractivity (defined by Floret) and further strong regularity conditions (introduced e.g. by Bierstedt and Meise) are all equivalent. This solves a problem that was folklore since around 1970. For inductive limits of Fréchet-Montel spaces we obtain even stronger results, in particular, Grothendieck's problem whether...

An associative law for infinite topological A-tensor product A-algebras

Kyriazis, Athanasios (1989)

Portugaliae mathematica

An Existence Result for Simple Inductive Limits of Interval Algebras.

Jesper Villadsen (1994)

Mathematica Scandinavica

Associated weights and spaces of holomorphic functions

Klaus Bierstedt, José Bonet, Jari Taskinen (1998)

Studia Mathematica

When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G \subset ℂ^{N}$ which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize...

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A Characterization of Totally Reflexive Fréchet Spaces.

A direct sum is holomorphically bornological with the topology induced by a cartesian product

A family of Kučera spaces

A local version of the Dauns-Hofmann theorem.

A Note on the Topology Associated with a Local Convex Space

A note on the topology associated with a locally convex space.

A version of the Bartle--Graves theorem for temperate functions.

Acyclic inductive spectra of Fréchet spaces

An associative law for infinite topological A-tensor product A-algebras

An Existence Result for Simple Inductive Limits of Interval Algebras.

Associated weights and spaces of holomorphic functions

Bemerkungen über unendlichdimensionale, separierte Limesvektorräume und Limesgruppen.

Boundaries in inductive limit topological algebras.

Bounded sets in fast complete inductive limits.

Caractérisations des b-espaces libres.

Central morphisms and envelopes of holomorphy.

Completeness of regular inductive limits.

Concerning holomorphy types for Banach spaces

Conditional Banach Spaces, Conditional Projections and Generalized Martingales.

Continous Norms on Locally Convex Strict Inductive Limit Spaces.

Currently displaying 1 – 20 of 86