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Spear Operators Between Banach Spaces

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Spear Operators Between Banach Spaces/ by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez.
Author:	Kadets, Vladimir.
other author:	Martín, Miguel.
Description:	XVII, 164 p. 5 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-3-319-71333-5
ISBN:	9783319713335

Spear Operators Between Banach Spaces
Kadets, Vladimir.

Spear Operators Between Banach Spaces[electronic resource] /by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez. - 1st ed. 2018. - XVII, 164 p. 5 illus.online resource. - Lecture Notes in Mathematics,22050075-8434 ;. - Lecture Notes in Mathematics,2144.

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.

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.

ISBN: 9783319713335

Standard No.: 10.1007/978-3-319-71333-5doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Spear Operators Between Banach Spaces
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