Spear operators between Banach spaces
Author(s)
Bibliographic Information
Spear operators between Banach spaces
（Lecture notes in mathematics, 2205）
Springer, c2018
Available at / 36 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||2205200037720707
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Note
Other authors: Miguel Martín, Javier Merí, Antonio Pérez
Pagination of later print (add errata): xvii, 161, E1
Includes bibliographical references (p. 153-157) and index
Description and Table of Contents
Description
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-Nikodym 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.
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.
by "Nielsen BookData"