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K -monotone Spaces between Spaces of Absolutely Summable Series

K -monotone Spaces between Spaces of Absolutely Summable Series 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

K -monotone Spaces between Spaces of Absolutely Summable Series

Forum Mathematicum , Volume 2 (2) – Jan 1, 1990

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References (16)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1990.2.73
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1990

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