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Alternate signs Banach-Saks property and real interpolation of operators

Author: Andrzej Kryczka
Journal: Proc. Amer. Math. Soc. 136 (2008), 3529-3537
MSC (2000): Primary 46B70, 47A30; Secondary 47B10
Published electronically: May 29, 2008
MathSciNet review: 2415037
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Abstract: In the space of bounded linear operators acting between Banach spaces we define a seminorm vanishing on the subspace of operators having the alternate signs Banach-Saks property. We obtain logarithmically convex-type estimates of the seminorm for operators interpolated by the Lions-Peetre real method. In particular, the estimates show that the alternate signs Banach-Saks property is inherited from a space of an interpolation pair $ (A_{0},A_{1})$ to the real interpolation spaces $ A_{\theta,p}$ with respect to $ (A_{0},A_{1})$ for all $ 0<\theta<1$ and $ 1<p<\infty$.

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Additional Information

Andrzej Kryczka
Affiliation: Institute of Mathematics, M. Curie-Skłodowska University, 20-031 Lublin, Poland

Keywords: Alternate signs Banach-Saks property, real interpolation method, spreading model.
Received by editor(s): July 11, 2007
Published electronically: May 29, 2008
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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