Extremal Problems for Operators in Banach Spaces Arising in the Study of Linear Operator Pencils |
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| Authors: | V. A. Khatskevich M. I. Ostrovskii V. S. Shulman |
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| Affiliation: | (1) Department of Mathematics, ORT Braude College, College Campus, P.O. Box 78, Karmiel, 21982, Israel;(2) Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, USA;(3) Department of Mathematics, Vologda State Technical University, 15 Lenina str., Vologda, 160000, Russia |
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| Abstract: | Inspired by some problems on fractional linear transformations the authors introduce and study the class of operators satisfying the condition where  stands for the spectral radius; and the class of Banach spaces in which all operators satisfy this condition, the authors call such spaces V-spaces. It is shown that many well-known reflexive spaces, in particular, such spaces as Lp(0,1) and Cp, are non-V-spaces if p  2; and that the spaces lp are V-spaces if and only if 1 < p <  . The authors pose and discuss some related open problems. |
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| Keywords: | Primary 47A10 47A30 Secondary 47B10 46B04 |
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