Product Factorable Multilinear Operators defined on Sequence Spaces

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Atıf İçin Kopyala

ERDOĞAN E.

Communications Faculty of Sciences University of Ankara SeriesSeries A1: Mathematics and Statistics, cilt.69, sa.2, ss.152-166, 2020 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 69 Sayı: 2
• Basım Tarihi: 2020
• Doi Numarası: 10.31801/cfsuasmas.752148
• Dergi Adı: Communications Faculty of Sciences University of Ankara SeriesSeries A1: Mathematics and Statistics
• Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.152-166
• Anahtar Kelimeler: Sequence spaces, multilinear operators, factorization, zero product preserving map, polynomials, ORTHOGONALLY ADDITIVE POLYNOMIALS, BILINEAR OPERATORS, MAPS, ALGEBRAS
• Marmara Üniversitesi Adresli: Evet

Özet

We prove a factorization theorem for multilinear operators acting in topological products of spaces of (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.