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Y. Brudnyi, S. Krein, E. Semenov (2002)
Interpolation of linear operatorsJournal of Soviet Mathematics, 42
H. Triebel (1978)
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The method of orbits in interpolation theory
Abstract. The purpose of this paper is to describe some Interpolation spaces with respect to compatible couples of Banach spaces of absolutely summable series in terms of the Kfunctional of Peetre. As a consequence, we obtain a large class of such couples that are not Calderon ones. 1980 Mathematics Subject Classification (1985 Revision): 46M35, 46E40, 46B25. 0. Introduction In the theory of Interpolation spaces those compatible couples of Banach spaces are particularly important whose Interpolation spaces are characterized by a monotonicity property in terms of the ^-functional of Peetre (such couples are called Kmonotone). In view of the work of Brudnyl and Krugljak [4] each Interpolation space with respect to a given jK-monotone compatible couple of Banach spaces is generated by the well-known real method of Interpolation. Couples whose all Interpolation spaces admit such a characterization have been termed Calderon couples. For any Banach space X, l^ (X) will denote the Banach space of all sequences {xv}v°°=-oo of Jf such that ||{x,}||lim = The main purpose of this paper is to describe all -monotone spaces between II(AQ) and /i(^41) that are of the form l^(A), where = (A^^A^ is an arbitrary compatible couple of Banach spaces and A
Forum Mathematicum – de Gruyter
Published: Jan 1, 1990
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