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arXiv · 2608.07024

A Note on Unbounded Convergences in Fremlin Projective Tensor Products

Omid Zabeti
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Abstract

We prove that the Fremlin projective tensor product of Banach lattices preserves unbounded norm convergence and unbounded absolute weak convergence of elementary tensors without any additional assumptions. The main tool is a tensor-lattice estimate controlling expressions of the form \[ \lvert x_{\alpha}\otimes y_{\beta}-x\otimes y\rvert \wedge w, \] where $w$ is positive in the tensor product. This provides a direct and simplified proof of permanence results previously obtained under extra hypotheses.

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Omid Zabeti. 2026-08-07. A Note on Unbounded Convergences in Fremlin Projective Tensor Products. https://arxiv.org/abs/2608.07024

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