Kadets, Vladimir Martin, Miguel Meri, Javier Perez, Antonio Spear operators between banach spaces 9783319713328

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Автор: Kadets, Vladimir Martin, Miguel Meri, Javier Perez, Antonio
Название: Spear operators between banach spaces
ISBN: 9783319713328
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Материаловедение

ISBN-10: 3319713329
Обложка/Формат: Paperback
Страницы: 164
Вес: 0.28 кг.
Дата издания: 19.03.2018
Серия: Lecture notes in mathematics
Язык: English
Издание: 1st ed. 2018
Иллюстрации: 5 illustrations, black and white; xvii, 164 p. 5 illus.
Размер: 154 x 234 x 18
Читательская аудитория: General (us: trade)
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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.
Дополнительное описание: 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

Spear operators between banach spaces, Kadets, Vladimir Martin, Miguel Meri, Javier Perez, Antonio