Spear Operators Between Banach Spaces

1. Auflage 2018
ISBN: 978-3-319-71332-8
Verlag: Springer International Publishing

Buch, Englisch, Band 2205, 164 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 289 g

Reihe: Lecture Notes in Mathematics

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  ? such that

? G+?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 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.

Zielgruppe

Research

Autoren/Hrsg.

Kadets, Vladimir

Pérez, Antonio

Martín, Miguel

Merí, Javier

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.