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Daugavet's equation and orthomorphisms


Author: Klaus D. Schmidt
Journal: Proc. Amer. Math. Soc. 108 (1990), 905-911
MSC: Primary 47B55; Secondary 46A40, 47A30
DOI: https://doi.org/10.1090/S0002-9939-1990-1002165-3
MathSciNet review: 1002165
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Abstract: The main result of this paper asserts that every Dunford-Pettis operator on an AL-space having no discrete elements satisfies Daugavet's equation $ \left\Vert {I + T} \right\Vert = 1 + \left\Vert T \right\Vert$; this extends a recent result of Holub on weakly compact operators. The proof is based on properties of orthomorphisms on a Banach lattice which also yield a short proof of another result of Holub concerning Daugavet's equation for bounded operators on an arbitrary AL- or AM-space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1002165-3
Keywords: Banach lattices, Dunford-Pettis operators, almost integral operators, orthomorphisms, Daugavet's equation
Article copyright: © Copyright 1990 American Mathematical Society

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