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
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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.

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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 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.

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