Stafney’s lemma holds for several “classical” interpolation methods
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Abstract:
Let $\left (B_{0},B_{1}\right )$ be a Banach pair. Stafney showed that one can replace the space $\mathcal {F}\left (B_{0},B_{1}\right )$ by its dense subspace $\mathcal {G}\left (B_{0},B_{1}\right )$ in the definition of the norm in the Calderón complex interpolation method on the strip if the element belongs to the intersection of the spaces $B_{i}$. We shall extend this result to a more general setting, which contains well-known interpolation methods: the Calderón complex interpolation method on the annulus, the Lions-Peetre real method (with different choices of norms), and the Peetre “$\pm$” method.References
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Additional Information
- Alon Ivtsan
- Affiliation: Department of Mathematics, Technion I.I.T., Haifa 32000, Israel
- Address at time of publication: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
- Email: aloniv@weizmann.ac.il
- Received by editor(s): August 31, 2010
- Received by editor(s) in revised form: December 13, 2010
- Published electronically: August 12, 2011
- Communicated by: Richard Rochberg
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 881-889
- MSC (2010): Primary 46B70; Secondary 46B45
- DOI: https://doi.org/10.1090/S0002-9939-2011-10974-2
- MathSciNet review: 2869072