Product factorable multilinear operators defined on sequence spaces

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:69 Issue:2
Product factorable multilinear operators defined on sequence spaces

Product factorable multilinear operators defined on sequence spaces

Pages : 1146-1160

View : 44 | Download : 17

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :We prove a factorization theorem for multilinear operators acting in topological products of spaces of insert ignore into journalissuearticles values(scalar); p-summable sequences through a product. It is shown that this class of multilinear operators called product factorable maps coincides with the well-known class of the zero product preserving operators. Due to the factorization, we obtain compactness and summability properties by using classical functional analysis tools. Besides, we give some isomorphisms between spaces of linear and multilinear operators, and representations of some classes of multilinear maps as n-homogeneous orthogonally additive polynomials.
Keywords : Sequence spaces, multilinear operators, factorization, zero product preserving map, polynomials

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