Espaces d'Interpolation Réels: Topologie et Géométrie

Beauzamy, Bernard

doi:10.1007/bfb0068827

Cited by 68 publications

(53 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We also compare the behaviour under interpolation of compact operators with the behaviour of weakly compact operators. As is well known (see the book by Beauzamy [1] or the paper by Mastyło [22]), if T : A 0 ∩ A 1 → B 0 + B 1 is weakly compact, then the interpolated operator is weakly compact as well. This is not the case in general for compact operators.…”

mentioning

confidence: 85%

Compact operators between K- and J-spaces

2005

View full text Add to dashboard Cite

Abstract. The paper establishes necessary and sufficient conditions for compactness of operators acting between general K-spaces, general J-spaces and operators acting from a J-space into a K-space. Applications to interpolation of compact operators are also given.1. Introduction. Interpolation of compact operators is one of the most active research areas in interpolation theory. Many authors have worked on this subject since the beginning of abstract interpolation theory in the early 1960s. During the last twenty years, new tools have been developed which are intimately related to the type of the interpolation method under consideration. Nowadays, still a lot of work is being done along different lines.Talking only about the real method, it was shown in the joint papers of one of the present authors with Edmunds and Potter [7], with Fernandez [8] and with Peetre [11] that properties of the vector-valued sequence spaces that come up when defining the real interpolation space (A 0 , A 1 ) θ,q are very useful to study the behaviour of compact operators under interpolation. These efforts culminated with Cwikel's [13] proof that if T : A → B withLater, the approach developed in [7,8,11] was used by Cobos, Kühn and Schonbek [9] to give a broad generalization of Cwikel's result, including a function parameter version and even compactness theorems for other interpolation methods. Techniques related to vector-valued sequence spaces have also turned out to be useful to study compactness in the multidimensional case and in the case of infinite families, as can be seen in the papers by Cobos and Peetre [12] and Carro and Peetre [5], respectively.

show abstract

mentioning

confidence: 85%

Compact operators between K- and J-spaces

2005

View full text Add to dashboard Cite

show abstract

“…The following result can be regarded as a generalization of the theorem of Beauzamy [6] about the reflexivity of Xo,p. Let us note that Lemma 5.2a) is also true for compact, weakly precompact (=Rosenthal) and Banach-Saks operators.…”

Section: Interpolation Of Weakly Compact Operatorsmentioning

confidence: 96%

Weakly compact operators and interpolation

Maligrańda

1992

Acta Appl Math

View full text Add to dashboard Cite

show abstract

“…[LT2]). Now if Q is isomorphic to 1 , we find, by [B,Prop. 2.3.3], that the inclusion E → F preserves an 1 -isomorphic copy.…”

Section: 38])mentioning

confidence: 98%

“…Assume that E ⊂ F is not weakly compact. Consider the real interpolation space (E, F ) θ,p for 0 < θ < 1, 1 < p < ∞, which is not reflexive by [B,Thm. 3.1].…”

Section: 38])mentioning

confidence: 99%

Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces

2009

View full text Add to dashboard Cite

Abstract. If G is the closure of L∞ in exp L2, it is proved that the inclusion between rearrangement invariant spaces E ⊂ F is strictly singular if and only if it is disjointly strictly singular andis not an interpolation space between L∞ and G it is proved that there exists another Marcinkiewicz space M (ψ) M (ϕ) with the property that the M (ψ) and M (ϕ) norms are equivalent on the Rademacher subspace. Applications are given and a question of Milman answered.

show abstract

Espaces d'Interpolation Réels: Topologie et Géométrie

Cited by 68 publications

References 0 publications

Compact operators between K- and J-spaces

Compact operators between K- and J-spaces

Weakly compact operators and interpolation

Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces

Contact Info

Product

Resources

About