Polynomials on Banach Lattices and UMD Constants with Decomposition of Spaces on Tensor Product

Abstract

We study the bounded variation , tensor products of Banach Lattices, tensor norms , operators in the category , the interpolation of injective or projective tensor products of Banach spaces . We give the decomposition of spaces of distributions induced by tensor product bases, homogeneous orthogonally additive polynomials on Banach Lattices , on spaces of continuous functions and positive tensor products . We determine the localized polynomial frames on the interval with Jacobi weights and on the ball. We also determine the sub-exponentially localized kernels and frames induced by orthogonal expansions. We show the operator space UMD property and constants for non-commutative 𝐿𝑝- spaces and for a class of iterate 𝐿𝑝(𝑙𝑞) spaces .