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Completely continuous and related multilinear operators

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Sam Houston State University, 77341, Huntsville, TX, USA

    David K. Ruch

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  1. David K. Ruch
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Research partially supported by a SHSU Research Enhancement Award

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Ruch, D.K. Completely continuous and related multilinear operators. Rend. Circ. Mat. Palermo 45, 377–396 (1996). https://doi.org/10.1007/BF02844510

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  • DOI: https://doi.org/10.1007/BF02844510

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