Best approximation by polynomial operators in banach spaces |
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| Authors: | Maria Sueli Marconi Roversi |
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| Institution: | Departamento De Matem′tica , Universidade Estadual de Campinas , Campinas, S.P, Brasil |
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| Abstract: | The problem of approximation in the space of bounded linear operators ? (E;G) between normed spaces E and G by compact operators has been extensively studied in the last few years. Recently Deutsch, Mach and Saatkamp (2]) have considered the problem of approximating elements of ?(E;G) by the subset K N(E;G) of operators whose range is at most N dimensional. We consider in this paper the problem of approximating operators (not necessarily linear) beteen normed spaces E and G by continuous homogeneous polynomials, and in particular by such polynomials which have finite-dimensional range. |
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