Displaying similar documents to “Tame Köthe Sequence Spaces are Quasi-Normable”

Some normability conditions on Fréchet spaces.

Tosun Terzioglu, Dietmar Vogt (1989)

Revista Matemática de la Universidad Complutense de Madrid

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We define two new normability conditions on Fréchet spaces and announce some related results.

Some seminorms on quasi *-algebras

Camillo Trapani (2003)

Studia Mathematica

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Different types of seminorms on a quasi *-algebra (𝔄,𝔄₀) are constructed from a suitable family ℱ of sesquilinear forms on 𝔄. Two particular classes, extended C*-seminorms and CQ*-seminorms, are studied in some detail. A necessary and sufficient condition for the admissibility of a sesquilinear form in terms of extended C*-seminorms on (𝔄,𝔄₀) is given.

The basic sequence problem

N. Kalton (1995)

Studia Mathematica

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We construct a quasi-Banach space X which contains no basic sequence.

Operators whose adjoints are quasi p-nuclear

J. M. Delgado, C. Piñeiro, E. Serrano (2010)

Studia Mathematica

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For p ≥ 1, a set K in a Banach space X is said to be relatively p-compact if there exists a p-summable sequence (xₙ) in X with K ⊆ ∑ ₙ α ₙ x ₙ : ( α ₙ ) ∈ B ℓ p ' . We prove that an operator T: X → Y is p-compact (i.e., T maps bounded sets to relatively p-compact sets) iff T* is quasi p-nuclear. Further, we characterize p-summing operators as those operators whose adjoints map relatively compact sets to relatively p-compact sets.

Bayoumi quasi-differential is not different from Fréchet-differential

Fernando Albiac, José Ansorena (2012)

Open Mathematics

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Unlike for Banach spaces, the differentiability of functions between infinite-dimensional nonlocally convex spaces has not yet been properly studied or understood. In a paper published in this Journal in 2006, Bayoumi claimed to have discovered a new notion of derivative that was more suitable for all F-spaces including the locally convex ones with a wider potential in analysis and applied mathematics than the Fréchet derivative. The aim of this short note is to dispel this misconception,...

Bayoumi Quasi-Differential is different from Fréchet-Differential

Aboubakr Bayoumi (2006)

Open Mathematics

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We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex