Completely continuous and related multilinear operators
Completely continuous multilinear operators are defined and their properties investigated. This class of operators is shown to form a closed multi-ideal. Unlike the linear case, compact multilinear operators need not be completely continuous. The completely continuous maps are shown to be the closure of a subspace of the finite rank operators. Hilbert-Schmidt operators are also considered. An application to finding error bounds for solutions of multipower equations is presented.
KeywordsBanach Space Continuous Operator Finite Rank Reflexive Banach Space Multilinear Operator
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- Antosik P., Swartz C.,Matrix Methods in Analysis, Lecture Notes in Mathematics 1113, Springer-Verlag, 1985.Google Scholar
- Argyros I. K.,On the approximation of solutions of compact operator equations in Banach space, Proyecciones,14 (1988), 29–46.Google Scholar
- Braunß A., Junek H.,Bilinear mappings and operator ideals, Rend. Circ. Mat. Palermo, Suppl.10 (1985), 25–35.Google Scholar
- Chandrasekhar S.,Radiative Transfer, Dover, New York, 1960.Google Scholar
- Pietsch A.,Ideals of multilinear functionals, Proc. of the II Intern. Conf. on Operator Ideals and their Applic. in Theoretical Physics, Leipzig, 1983.Google Scholar
- Pietsch A.,Operator Ideals, Deutscher Verlag der Wissenschaften, Berlin, 1979.Google Scholar
- Wang J.,A cubic spline wavelet basis of C[0,1], preprint, 1994.Google Scholar