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Some remarks on the Daugavet equation


Author: P. Wojtaszczyk
Journal: Proc. Amer. Math. Soc. 115 (1992), 1047-1052
MSC: Primary 47B07; Secondary 46B20, 47A30, 47B48
DOI: https://doi.org/10.1090/S0002-9939-1992-1126202-2
MathSciNet review: 1126202
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Abstract: We show that direct sums in $ {l_1}$ and $ {l_\infty }$ sense of Banach spaces that satisfy the Daugavet Equation (1) also satisfy it. We also show that most uniform algebras satisfy (1) for weakly compact operators.


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

  • [A] Yuri Abramovich, New classes of spaces on which compact operators satisfy the Daugavet equation, J. Operator Theory (to appear). MR 1203038 (94a:47061)
  • [D] I. K. Daugavet, A property of compact operators in the space $ C$, Uspekhi Mat. Nauk 18 (1963), 157-158. (Russian) MR 0157225 (28:461)
  • [DU] J. Diestel and J. J. Uhl, Vector measures, Math. Surveys Monographs, vol. 15, Amer. Math. Soc., Providence, RI, 1977. MR 0453964 (56:12216)
  • [G] T. W. Gamelin, Uniform algebras, Prentice Hall, Englewood Cliffs, NJ, 1969. MR 0410387 (53:14137)
  • [M] H. Milne, Banach space properties of uniform algebras, Bull. London Math. Soc. 4 (1972), 323-326. MR 0322485 (48:847)
  • [PP] M. Plichko Anatolii and M. Popov Mikhail, Symmetric function spaces on atomless probability spaces, Dissertationes Math. 306 (1990). MR 1082412 (92f:46032)
  • [W] P. Wojtaszczyk, Banach spaces for analysts, Cambridge Stud. Adv. Math., vol. 25, Cambridge Univ. Press, Cambridge, 1991. MR 1144277 (93d:46001)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1126202-2
Article copyright: © Copyright 1992 American Mathematical Society

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