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

Author(s): R. V. Shvydkoy
Journal: Proc. Amer. Math. Soc. 130 (2002), 773-777.
MSC (2000): Primary 47B38; Secondary 46E30.
Posted: August 28, 2001
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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.

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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: 10.1090/S0002-9939-01-06179-2
PII: S 0002-9939(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
Posted: August 28, 2001
Additional Notes: The author wishes to thank V. M. Kadets for stimulating discussions and useful remarks.
Communicated by: Dale Alspach
Copyright of article: Copyright 2001, American Mathematical Society

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