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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stafney's lemma holds for several ``classical'' interpolation methods


Author: Alon Ivtsan
Journal: Proc. Amer. Math. Soc. 140 (2012), 881-889
MSC (2010): Primary 46B70; Secondary 46B45
Published electronically: August 12, 2011
MathSciNet review: 2869072
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10974-2
PII: S 0002-9939(2011)10974-2
Keywords: Interpolation spaces, Banach sequence spaces
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.