Spear Operators Between Banach Spaces pp 83-95 | Cite as
Further Results
Chapter
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Abstract
Our goal here is to complement the previous chapter with some interesting results. We characterize lush operators when the domain space has the Radon-Nikodým Property or the codomain space is Asplund, and we get better results when the domain or the codomain is finite-dimensional or when the operator has rank one. Further, we study the behaviour of lushness, spearness and the aDP with respect to the operation of taking adjoint operators.
References
- 20.R. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodym Property. Lecture Notes in Mathematics, vol. 993 (Springer, Berlin, 1983)CrossRefGoogle Scholar
- 21.K. Boyko, V. Kadets, M. Martín, D. Werner, Numerical index of Banach spaces and duality. Math. Proc. Camb. 142, 93–102 (2007)MathSciNetCrossRefGoogle Scholar
- 53.P. Harmand, D. Werner, D. Werner, M-Ideals in Banach Spaces and Banach Algebras. Lecture Notes in Mathematics, vol. 1547 (Springer, Berlin, 1993)Google Scholar
- 61.V. Kadets, R. Shvidkoy, G. Sirotkin, D. Werner, Banach spaces with the Daugavet property. Trans. Am. Math. Soc. 352, 855–873 (2000)MathSciNetCrossRefGoogle Scholar
- 67.V. Kadets, M. Martín, J. Merí, V. Shepelska, Lushness, numerical index one and duality. J. Math. Anal. Appl. 357, 15–24 (2009)MathSciNetCrossRefGoogle Scholar
- 94.M. Martín, T. Oikhberg, An alternative Daugavet property. J. Math. Anal. Appl. 294, 158–180 (2004)MathSciNetCrossRefGoogle Scholar
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