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This 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.
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Spear Operators Between Banach Spaces.
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Spear Operators Between Banach Spaces (eng)
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Spear operators between Banach spaces. Lecture notes in mathematics; Bd. 2205.
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Spear Operators Between Banach Spaces (Lecture Notes in Mathematics, 2205)
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Spear Operators Between Banach Spaces
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Springer International Publishing Apr 2018, 2018
ISBN 10: 3319713329
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This 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 Y there exists a modulus-one scalar such that G+ 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 . 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. 184 pp. Englisch. Seller Inventory # 9783319713328
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Spear Operators Between Banach Spaces
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Spear Operators Between Banach Spaces: 2205 (Lecture Notes in Mathematics)
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