| Spear Operators Between Banach Spaces 2018 Edition Contributor(s): Kadets, Vladimir (Author), Martín, Miguel (Author), Merí, Javier (Author) |
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ISBN: 3319713329 ISBN-13: 9783319713328 Publisher: Springer OUR PRICE: $47.49 Product Type: Paperback - Other Formats Published: April 2018 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Calculus |
| Dewey: 515 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.39" H x 6.14" W x 9.21" (0.58 lbs) 164 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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 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. |