Spear Operators Between Banach Spaces

By Javier Merí, Miguel Martin, Vladimir Kadets

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 G+ωTǁ = 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 L₁. The relationships with the Radon-Nikod?m 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.

• Format: Paperback
• Language: English
• ISBN: 3319713329
• ISBN13: 9783319713328
• Release Date: April 2018
• Publisher: Springer
• Length: 164 Pages
• Weight: 0.58 lbs.
• Dimensions: 0.4" x 6.1" x 9.2"