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Spear Operators Between Banach Spaces de Vladimir Kadets

Spear Operators Between Banach Spaces: Lecture Notes in Mathematics, cartea 2205

Autor Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
en Limba Engleză Paperback – 17 apr 2018
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.
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Specificații

ISBN-13: 9783319713328
ISBN-10: 3319713329
Pagini: 163
Ilustrații: XVII, 164 p. 5 illus.
Dimensiuni: 155 x 235 x 18 mm
Greutate: 0.26 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

1. Introduction.- 2. Spear Vectors and Spear Sets.- 3. Spearness, the aDP and Lushness.- 4. Some Examples in Classical Banach Spaces.- 5. Further Results.- 6. Isometric and Isomorphic Consequences.- 7. Lipschitz Spear Operators.- 8. Some Stability Results.- 9. Open Problems.

Recenzii

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

Textul de pe ultima copertă

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.

Caracteristici

No prerequisites required to fully understand an active research line Full proofs of all the main results Systematic study of spear operators for the first time in a book