A NONCOMMUTATIVE GRETSKY—OSTROY THEOREM AND ITS APPLICATIONS

JINCH AO HUANG; MARAT PLIEV; FEDOR SUKOCHEV

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A NONCOMMUTATIVE GRETSKY—OSTROY THEOREM AND ITS APPLICATIONS

机译：A NONCOMMUTATIVE GRETSKY—OSTROY THEOREM AND ITS APPLICATIONS

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Let H be a separable Hilbert space and let B(H) be the *-algebra of all bounded linear operators on H. In the present paper, we prove that a positive/regular operator from L_1(0,1) into an arbitrary separable operator ideal in B(H) is necessarily Dunford-Pettis, extending and strengthening results due to Gretsky and Ostroy Glasgow Math. J. 28 (1986), pp. 113—114, and Holub Proc. Amer. Math. Soc. 104 (1988), pp. 89-95. Consequently, for an arbitrary atomless von Neumann algebra M and an arbitrary KB-ideal C_E in B(H), the predual M* of M is not isomorphic to any subspace of C_E. This observation complements several earlier results.

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《Proceedings of the American Mathematical Society》 |2023年第3期|1147-1155|共9页
作者
JINCH AO HUANG; MARAT PLIEV; FEDOR SUKOCHEV;
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作者单位

Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China;

Southern Mathematical Institute of the Russian Academy of Sciences, Vladikavkaz, 362027 Russia;

School of Mathematics and Statistics, University of New South Wales, Kensington 2052, Australia;

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正文语种英语
中图分类数学;
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Dunford-Pettis operator; predual of a von Neumann algebra; isomorphic embedding;

A NONCOMMUTATIVE GRETSKY—OSTROY THEOREM AND ITS APPLICATIONS

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