The uniqueness of the solution to inverse interpolation problems
泛函分析
2007-05-23 v1
摘要
We prove that an arbitrary Banach couple is uniquely determined by the collection of intermediate spaces that are interpolation spaces for the operators of rank one. From this we deduce a confirmation to the conjecture by Yu. A. Brudnyi and N.Ya. Kruglyak that a Banach couple is uniquely determined by the collection of all its interpolation spaces. Some relevant problems are also analized.
关键词
引用
@article{arxiv.math/9902108,
title = {The uniqueness of the solution to inverse interpolation problems},
author = {Lidia V. Veselova and Oleg E. Tikhonov},
journal= {arXiv preprint arXiv:math/9902108},
year = {2007}
}
备注
Revised and translated form of "Research Institute of Mathematics and Mechanics, Preprint no. 95-2, Kazan Mathematics Foundation, Kazan, 1995. (Russian)"