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The largest linear space of operators satisfying the Daugavet equation in $ L_{1}$


Author: R. V. Shvydkoy
Journal: Proc. Amer. Math. Soc. 130 (2002), 773-777
MSC (2000): Primary 47B38; Secondary 46E30.
DOI: https://doi.org/10.1090/S0002-9939-01-06179-2
Published electronically: August 28, 2001
MathSciNet review: 1866033
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Abstract:

We find the largest linear space of bounded linear operators on $L_1(\Omega)$ that, being restricted to any $L_1(A)$, $A\subset \Omega $, satisfy the Daugavet equation.


References [Enhancements On Off] (What's this?)

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Additional Information

R. V. Shvydkoy
Affiliation: Department of Mathematics, University of Missouri - Columbia, Columbia, Missouri 65211
Email: shvidkoy@math.missouri.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06179-2
Keywords: Daugavet equation, weakly compact operators, narrow operators.
Received by editor(s): November 12, 1999
Received by editor(s) in revised form: September 15, 2000
Published electronically: August 28, 2001
Additional Notes: The author wishes to thank V. M. Kadets for stimulating discussions and useful remarks.
Communicated by: Dale Alspach
Article copyright: © Copyright 2001 American Mathematical Society

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