Alternate signs Banach-Saks property and real interpolation of operators

Kryczka, Andrzej

doi:10.1090/S0002-9939-08-09562-2

Alternate signs Banach-Saks property and real interpolation of operators
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Proc. Amer. Math. Soc. 136 (2008), 3529-3537 Request permission

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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