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" Spear operators between Banach spaces / "
Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez.
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BL
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| Record Number
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864247
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| Main Entry
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Kadet︠s︡, V. M., (Vladimir M.)
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| Title & Author
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Spear operators between Banach spaces /\ Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2018.
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| Series Statement
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Lecture notes in mathematics,; 2205
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| Page. NO
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1 online resource (xv, 164 pages) :: color illustrations
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| ISBN
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3319713337
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: 9783319713335
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3319713329
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9783319713328
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Historical Introduction: A Walk on the Results for Banach Spaces with Numerical Index 1 -- Spear Vectors and Spear Sets -- Three Definitions for Operators: Spearness, the Alternative Daugavet Property, and Lushness -- Some Examples in Classical Banach Spaces -- Further Results -- Isometric and Isomorphic Consequences -- Lipschitz Spear Operators -- Some Stability Results -- Open Problems -- Erratum to: Spear Operators Between Banach Spaces.
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| Abstract
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His monograph is devoted to the study of spear operators, that is, bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrightarrow Y$ there exists a modulus-one scalar $\omega$ such that $\|G + \omega\, T\|=1+ \|T\|$. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on $L_1$. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.--Provided by publisher.
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| Subject
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Banach spaces.
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Operator theory.
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Banach spaces.
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Calculus mathematical analysis.
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Mathematics-- Mathematical Analysis.
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Operator theory.
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| Dewey Classification
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515/.732
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| LC Classification
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QA322.2
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| Added Entry
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Martín, Miguel, (Martín Suárez)
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Merí, Javier
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Pérez, Antonio, (Pérez Hernández),1989-
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