Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Alternate signs Banach-Saks property and real interpolation of operators

Author(s): Andrzej Kryczka
Journal: Proc. Amer. Math. Soc. 136 (2008), 3529-3537.
MSC (2000): Primary 46B70, 47A30; Secondary 47B10
Posted: 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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