Spatial numerical ranges of elements of Banach algebras.
Gaur, A.K., Husain, T. (1989)
International Journal of Mathematics and Mathematical Sciences
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Gaur, A.K., Husain, T. (1989)
International Journal of Mathematics and Mathematical Sciences
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Miguel Martín (2000)
Extracta Mathematicae
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Miguel Martín, Rafael Payá (2000)
Studia Mathematica
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We show that the numerical index of a -, -, or -sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.
A. Torgašev (1975)
Matematički Vesnik
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Karahanyan, M.I. (2005)
Lobachevskii Journal of Mathematics
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Mohammad Ali Ardalani (2014)
Studia Mathematica
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We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.
María D. Acosta, M. Ruiz Galán (2000)
Extracta Mathematicae
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In this note we deal with a version of James' Theorem for numerical radius, which was already considered in [4]. First of all, let us recall that this well known classical result states that a Banach space satisfying that all the (bounded and linear) functionals attain the norm, has to be reflexive [16].
Abdollahi, Abdolaziz, Heydari, Mohammad Taghi (2011)
International Journal of Mathematics and Mathematical Sciences
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María D. Acosta (1990)
Extracta Mathematicae
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E. Cancès, S. Labbé (2012)
ESAIM: Proceedings
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Anita Dobek (2008)
Discussiones Mathematicae Probability and Statistics
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