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Spear Operators Between Banach Spaces

Miguel Martin author Antonio Perez author Vladimir Kadets author Javier Merí author

Format:Paperback

Publisher:Springer International Publishing AG

Published:17th Apr '18

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Spear Operators Between Banach Spaces cover

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 GTǁ = 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 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.

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

ISBN: 9783319713328

Dimensions: unknown

Weight: 454g

164 pages

1st ed. 2018