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- W2126194914 abstract "Consider the following possible properties which a Banach space X may have: (P): If ( x i ) and ( y j ) are bounded sequences in X such that for all n ≥ 1 and for every continuous n-homogeneous polynomial P on X, P ( x j ) − ( y j ) → 0, then Q ( x j − y j ) → 0 for all m ≥ 1 and for every continuous m-homogeneous polynomial Q on X . (RP): If ( x j )and ( y j ) are bounded sequences in X such that for all n ≥ 1 and for every continuous n-homogeneous polynomial P on X, P ( x j − y j ) → 0, then Q ( x j ) − Q ( y j ) → 0 for all m ≥ 1 and for every continuous m-homogeneous polynimial Q on X. We study properties ( P ) and ( RP ) and their relation with the Schur proqerty, Dunford-Pettis property, Λ, and others. Several applications of these properties are given." @default.
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- W2126194914 date "1995-12-01" @default.
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- W2126194914 title "Estimates by polynomials" @default.
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- W2126194914 doi "https://doi.org/10.1017/s0004972700014957" @default.
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