Spear Operators Between Banach Spaces - Couverture souple

Kadets, Vladimir; Martin, Miguel; Mer, Javier; Prez, Antonio

Couverture souple

ISBN 10 : 3319713329 ISBN 13 : 9783319713328

Editeur : Springer, 2018

Synopsis

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 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.

A propos du livre

À propos de l'auteur

Vladimir Kadets has authored two monographs and more than 100 articles in peer-reviewed journals, mainly in Banach space theory: sequences and series, bases, vector-valued measures and integration, measurable multi-functions and selectors, isomorphic and isometric structures of Banach spaces, operator theory. In 2005 he received the State Award of Ukraine in Science and Technology to honour his research. The present book reflects the author's teaching experience in the field, spanning over more than 20 years.

À propos de la quatrième de couverture

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 3319713329
• ISBN 13: 9783319713328
• Reliure: Broché
• Numéro d'édition: 1
• Nombre de pages: 164
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne