Spear Operators Between Banach Spaces

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Calculus
Cover of the book Spear Operators Between Banach Spaces by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez ISBN: 9783319713335
Publisher: Springer International Publishing Publication: April 16, 2018
Imprint: Springer Language: English
Author: Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
ISBN: 9783319713335
Publisher: Springer International Publishing
Publication: April 16, 2018
Imprint: Springer
Language: English

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**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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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**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.

More books from Springer International Publishing

Cover of the book Medical Ethics Education: An Interdisciplinary and Social Theoretical Perspective by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Enterprise Interoperability VII by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Brachytherapy by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Transport Processes at Fluidic Interfaces by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Multiscale Modelling in Sheet Metal Forming by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Deviance in Social Media and Social Cyber Forensics by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Intelligence Science and Big Data Engineering by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Bionanocomposites for Packaging Applications by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Novel Measurement and Assessment Tools for Monitoring and Management of Land and Water Resources in Agricultural Landscapes of Central Asia by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Novel Methods in Computational Finance by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Chromatin Architecture by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Computational Science and Its Applications – ICCSA 2018 by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book European Regulation of Medical Devices and Pharmaceuticals by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Topological Data Analysis for Scientific Visualization by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
Cover of the book Brain-Computer Interface Research by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy