Calderón constants of finite-dimensional couples
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The Calderón constant æ(\(\bar X\)) is a numerical invariant of finite-dimensional Banach couple\(\bar X = (X_0 ,X_1 )\) measuring its interpolation property with respect to linear operators acting in\(\bar X\). In the paper we prove the duality relation æ(\(\bar X\))≈ æ(\(\bar X\) *)and calculate the asymptotic behavior of æ(\(\bar X\)) as dim\(\bar X \to \infty \) for a few “classical” Banach couples.
KeywordsBanach Space Linear Operator Bounded Linear Operator Banach Lattice Absolute Constant
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- [B] T. Bychkova,Couples without C-properties, inInvestigations in the Theory of Functions of Several Variables, Yaroslavl, 1990, pp. 48–51 (in Russian).Google Scholar
- [BK] Y. Brudnyi and N. Krugljak,Interpolation Functors and Interpolation Spaces, North-Holland, Amsterdam-New York-Oxford-Tokyo, 1992, 718 pp.Google Scholar
- [CN] M. Cwikel and P. Nilsson,Interpolation of weighted Banach lattices, Memoirs of the American Mathematical Society (to appear).Google Scholar
- [M] B. S. Mitiagin,An interpolation theorem for modular spaces, Matematicheskii Sbornik66 (1965), 473–482 (in Russian).Google Scholar