## $l_\infty$ and interpolation between Banach lattices

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- by Nahum Zobin and Veronica Zobin PDF
- Proc. Amer. Math. Soc.
**125**(1997), 827-833 Request permission

## Abstract:

We study the possibility of obtaining the $l_{\infty }$-norm by an interpolation method starting from a couple of Banach lattice norms. We describe all couples of Banach lattice norms in ${\mathbb {R}}^{n}$ such that the $l_{\infty }$-norm is a strict interpolation norm between them. Further we consider the possibility of obtaining the $l_{\infty }$-norm by any method which guarantees interpolation of not only linear operators ( = bilinear forms on ${\mathbb {R}}^{n}\times {\mathbb {R}}^{n})$ but also of all polylinear forms. Here we show that either one of the initial norms has to be proportional to the $l_{\infty }$-norm, or both have to be weighted $l_{\infty }$-norms.## References

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## Additional Information

**Nahum Zobin**- Affiliation: Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124
- Address at time of publication: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
- Email: zobin@math.miami.edu, zobin@math.ohio-state.edu
**Veronica Zobin**- Affiliation: Department of Mathematics, Technion – I.I.T., Haifa, 32000, Israel
- Address at time of publication: Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124
- Email: zobin@math.miami.edu
- Received by editor(s): December 1, 1994
- Received by editor(s) in revised form: September 13, 1995
- Additional Notes: The research of the first author was partially supported by grants from the Ministry of Absorption, the Ministry of Science and Technology (Israel) and by the Rashi Foundation (France-Israel). The research of the second author was partially supported by a grant from the Ministry of Science, Israel, and “Maagara"—a special project for absorption of new immigrants—at the Department of Mathematics, Technion, Haifa, Israel.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 827-833 - MSC (1991): Primary 46M35
- DOI: https://doi.org/10.1090/S0002-9939-97-03646-0
- MathSciNet review: 1353410