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Bases In Spaces Of Regular Multilinear Operators And Homogeneous Polynomials On Banach Lattices, Khazhak Varazdat Navoyan
Bases In Spaces Of Regular Multilinear Operators And Homogeneous Polynomials On Banach Lattices, Khazhak Varazdat Navoyan
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For Banach lattices E1,…, Em and F with 1-unconditional bases, we show that the monomial sequence forms a 1-unconditional basis of Lr(E1,…, Em;F), the Banach lattice of all regular m-linear operators from E1×···× Em to F, if and only if each basis of E1,…,Em is shrinking and every positive m-linear operator from E 1×···×Em to F is weakly sequentially continuous. As a consequence, we obtain necessary and sufficient conditions for which the m-fold Fremlin projective tensor product E1⊗ |π|··· ⊗|π|E m (resp. the m-fold positive injective tensor product E1⊗|ϵ|··· ⊗ |ϵ|Em) has a shrinking basis or a boundedly complete basis. …