Extrapolation properties of closed operator ideals

Fernández─Cabrera, Luz M.; Martı́nez, Antón

doi:10.5186/aasfm.2013.3821

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Extrapolation Results1

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2013

2014

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“…A measure of weak noncompactness for operators extrapolated by ∆ p -and Σ p -methods of Jawerth and Milman [21] with 1 < p < ∞ was estimated in [26] (see also [35]). A general qualitative approach to extrapolation properties of closed operator ideals was recently presented by Fernández-Cabrera and Martínez in [15].…”

Section: Extrapolation Resultsmentioning

confidence: 99%

Mean separations in Banach spaces under abstract interpolation and extrapolation

Kryczka

2013

Journal of Mathematical Analysis and Applications

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logarithmic space a b s t r a c tWe introduce the mean separation for bounded sequences in Banach spaces and the related seminorm for bounded linear operators. The introduced quantities are closely related to the geometric characterizations of the Banach-Saks property and the alternate signs Banach-Saks property. We investigate the behavior of the mean separations for a class of operators between vector-valued Banach sequence spaces E(X ν ), providing that a Banach sequence lattice E has the Banach-Saks property. We estimate the mean separations for operators under abstract interpolation and extrapolation methods. In particular, we obtain quantitative and qualitative results on the heredity of the Banach-Saks properties under these methods.

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