Alternate signs Banach-Saks property and real interpolation of operators
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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 $1<p<\infty$.References
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Additional Information
- Andrzej Kryczka
- Affiliation: Institute of Mathematics, M. Curie-Skłodowska University, 20-031 Lublin, Poland
- Email: andrzej.kryczka@umcs.lublin.pl
- Received by editor(s): July 11, 2007
- Published electronically: May 29, 2008
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3529-3537
- MSC (2000): Primary 46B70, 47A30; Secondary 47B10
- DOI: https://doi.org/10.1090/S0002-9939-08-09562-2
- MathSciNet review: 2415037