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l(Φ,φ) operators and (Φ,φ)-spaces.

Nicolae Tita (1979)

Collectanea Mathematica

A new class of linear and bounded operators is introduced. This class is more general than the classes of operators from [4], [5] and [8]. Using this class lΦ,φ we also introduce a class of locally convex spaces which is more general than the classes of the nuclear spaces [2], [3] and φ-nuclear spaces [6]. For this class of operators similar properties are established to those of the well known classes lp, lφ, lΦ and also the stability of the tensor product is proved. The stability of the tensor...

Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces

Christopher Boyd (1993)

Studia Mathematica

For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that G ( U ) i ' = ( ( U ) , τ δ ) . Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the τ 0 and τ ω topologies on ℋ (U).

On Cental Morphisms

Athanassios Kyriazis (1992)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On interpolation of bilinear operators by methods associated to polygons

Fernando Cobos, José María Cordeiro, Antón Martínez (1999)

Bollettino dell'Unione Matematica Italiana

Stabiliamo teoremi di interpolazione bilineare per una combinazione dei metodi di K - e J -interpolazione associati ai poligoni, e per il J -metodo. Mostriamo che un simile risultato fallisce per il K -metodo, e diamo applicazioni all'interpolazione di spazi di operatori.

On operator ideals related to (p,σ)-absolutely continuous operators

J. López Molina, E. Sánchez Pérez (2000)

Studia Mathematica

We study tensor norms and operator ideals related to the ideal P p , σ , 1 < p < ∞, 0 < σ < 1, of (p,σ)-absolutely continuous operators of Matter. If α is the tensor norm associated with P p , σ (in the sense of Defant and Floret), we characterize the ( α ' ) t -nuclear and ( α ' ) t - integral operators by factorizations by means of the composition of the inclusion map L r ( μ ) L 1 ( μ ) + L p ( μ ) with a diagonal operator B w : L ( μ ) L r ( μ ) , where r is the conjugate exponent of p’/(1-σ). As an application we study the reflexivity of the components of the ideal...

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