About this book
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.
Banach Space Bounded Linear Operator Daugavet Equation Daugavet Property, Alternative Daugavet Property Numerical Range of Operators Numerical Index of Banach Spaces Lush Space Spear Operator Lipschitz Operator
- DOI https://doi.org/10.1007/978-3-319-71333-5
- Copyright Information Springer International Publishing AG, part of Springer Nature 2018
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-71332-8
- Online ISBN 978-3-319-71333-5
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- About this book