Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0935.46060
Cobos, F.; Fernández-Martínez, P.; Martínez, A.
On reiteration and the behaviour of weak compactness under certain interpolation methods. (English)
[J] Collect. Math. 50, No.1, 53-72 (1999). ISSN 0010-0757; ISSN 2038-4815/e

This article deals with K- and J-spaces defined by means of polygons. First, we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We show that if just one restriction of the operator $T$ is weakly compact, then the interpolation operator from a J-space into a K-space also has this property, but in general this is not the case if we consider $T$ acting between two J-spaces or two K-spaces. For these cases we prove that the interpolated operator is weakly compact provided that all but two restrictions of $T$ (located in adjacent vertices of the polygon) are weakly compact. We also show by means of examples that these results are best possible.
[F.Cobos (Madrid)]

MSC 2000:: *46M35 Abstract interpolation of topological linear spaces
46B70 Interpolation between normed linear spaces
47B07 Operators defined by compactness properties

Keywords: means of polygons; reiteration formulae; weakly compact operators; interpolation operator from a J-space into a K-space

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]