Spear Operators Between Banach Spaces

By: Antonio Perez, Vladimir Kadets, Miguel Martin, Javier Meri

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Paperback | 17 April 2018

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182 Pages

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15.4 x 23.4 x 1.8

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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 → Y there exists a modulus-one scalar ω such that

ǁ G+ωTǁ = 1 + ǁTǁ.

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 L₁. 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.

Industry Reviews

"This book will certainly be of interest to all researchers who specialise in Banach space theory." (Jan-David Hardtke, zbMATH 1415.46002, 2019)

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