Quojection and Prequojections

We characterize tame pairs (X, Y ) of Fréchet spaces where either X or Y is a power series space. For power series spaces of finite type, we get the well-known conditions of (DN)-(Ω) type. On the other hand, for power series spaces of infinite type, surprisingly, tameness implies boundedness of every linear and continuous operator. Next, we prove that every tame Fréchet space is quasi-normable. This result extends earlier result of the author valid only for Köthe sequence spaces.

Section: From (25) It Follows Thatmentioning

confidence: 99%

“…In fact, X is a quojection if and only if it is a quotient of a countable product of Banach spaces (see [5]). A Fréchet space X is called a prequojection (see [11,Prop. 2.1]) if its bidual X is a quojection.…”

Section: From (25) It Follows Thatmentioning

confidence: 99%

On tame pairs of Fréchet spaces

Piszczek

2009

“…In particular, every quojection is a prequojection. The reader is referred to [7], [10], [12], [15] for more information on quasinormable spaces and to [4], [13] for the subclasses of quojections and prequojections.…”

Section: Preliminariesmentioning

confidence: 99%

On the bidual of quasinormable Fréchet algebras

Podara

2011

It is known that the bidual of a quasinormable Fréchet space E with local Banach spaces (En ) n ∈N is topologically isomorphic to the inverse limit of E n n ∈N . With the aid of the Arens product and by homological means, we prove that the previous result is equally valid for quasinormable Fréchet m-convex algebras. This allows showing that the bidual of a σ-C * -algebra equipped with the Arens product is a σ-C * -algebra and presenting a new direct proof of a result on acyclic spectra due to Palamodov.

“…Quojections have a representation as quotients of countable products of Banach spaces, and they are in particular quasinormable. We refer the reader to Metafune, Moscatelli [16] for a survey on quojections and related classes of Fréchet spaces.…”

Section: Introductionmentioning

confidence: 99%

Dense subspaces of quasinormable spaces

Bonet

Dierolf

Aye

2006

Dense linear subspaces of quasinormable Fréchet spaces need not be quasinormable, as an example due to J. Bonet and S. Dierolf proved. A characterization of the quasinormability of dense linear subspaces of quasinormable locally convex spaces and several consequences are given. Moreover, an example of a dense linear subspace of a countable direct sum of Banach spaces, which is not quasinormable, is provided.