Spear Operators Between Banach Spaces

• Main Authors: Kadets, Vladimir (Author, http://id.loc.gov/vocabulary/relators/aut), Martín, Miguel (http://id.loc.gov/vocabulary/relators/aut), Merí, Javier (http://id.loc.gov/vocabulary/relators/aut), Pérez, Antonio (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Lecture Notes in Mathematics, 2205
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Analysis.

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 co...

Table of Contents:

• 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.