03296nam 22005655 450 99646654130331620200702065037.03-319-71333-710.1007/978-3-319-71333-5(CKB)4100000003359227(DE-He213)978-3-319-71333-5(MiAaPQ)EBC6304019(MiAaPQ)EBC5578306(Au-PeEL)EBL5578306(OCoLC)1032303008(PPN)226696340(EXLCZ)99410000000335922720180416d2018 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierSpear Operators Between Banach Spaces[electronic resource] /by Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XVII, 164 p. 5 illus.)Lecture Notes in Mathematics,0075-8434 ;22053-319-71332-9 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.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 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 $L_1$. The relationships with the Radon-Nikodým 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.Lecture Notes in Mathematics,0075-8434 ;2205Mathematical analysisAnalysis (Mathematics)Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Mathematical analysis.Analysis (Mathematics).Analysis.515.724Kadets Vladimirauthttp://id.loc.gov/vocabulary/relators/aut59669Martín Miguelauthttp://id.loc.gov/vocabulary/relators/autMerí Javierauthttp://id.loc.gov/vocabulary/relators/autPérez Antonioauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996466541303316Spear Operators Between Banach Spaces2283993UNISA