REAL INTERPOLATION AND COMPACT LINEAR-OPERATORS

被引：24

作者：

COBOS, F

EDMUNDS, DE

POTTER, AJB

机构：

[1] UNIV SUSSEX,DIV MATH,BRIGHTON BN1 9QH,E SUSSEX,ENGLAND

[2] UNIV ABERDEEN,DEPT MATH,ABERDEEN AB9 2TY,SCOTLAND

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1990年 / 88卷 / 02期

关键词：

D O I：

10.1016/0022-1236(90)90110-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if T: A0 → B0 is compact and T: A1 → B1 is compact (or T: A1 → B1 is bounded and {A figure is presented}, then given any θ and q with 0 < θ < 1 and 0 < q≤ ∞, it follows that T: (A0, A1)0,q → (B0, B1)0,q, is also compact. Here (A0, A1)0,q and (B0, B1)0,q are the usual real interpolation spaces. © 1990.

引用

页码：351 / 365

页数：15

共 12 条

[1]

BEAUZAMY B, 1978, SPRINGER LECT NOTES, V666

[2]

Bergh J., 1976, INTERPOLATION SPACES, V223

[3]

Davis W. J., 1974, Journal of Functional Analysis, V17, P311, DOI 10.1016/0022-1236(74)90044-5

[4] FUNCTION PARAMETER IN CONNECTION WITH INTERPOLATION OF BANACH-SPACES [J].

GUSTAVSSON, J .

MATHEMATICA SCANDINAVICA, 1978, 42 (02) :289-305

[5] INTERPOLATION BY REAL METHOD PRESERVES COMPACTNESS OF OPERATORS [J].

HAYAKAWA, K .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1969, 21 (02) :189-+

[6]

Kantorovich LV, 1982, FUNCTIONAL ANAL

[7]

KRASNOSELSKII MA, 1960, SOV MATH DOKL, V1, P229

[8]

Lions J.-L., 1964, I HAUTES ETUDES SCI, P5, DOI 10.1007/BF02684796

[9]

MERUCCI C, 1984, SPRINGER LECT NOTES, V1070, P183

[10]

Peetre J., 1968, NOTAS MAT, V39, P1

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