Diagonals of injective tensor products of Banach lattices with bases

TL;DR

This paper investigates the structure of diagonals in injective tensor products of Banach lattices, establishing isometric isomorphisms and unconditional basic sequences, thereby advancing understanding of tensor product geometry.

Contribution

It demonstrates that diagonal spaces of injective tensor products are pairwise isometrically isomorphic and that tensor diagonals form 1-unconditional basic sequences in specific tensor products.

Findings

Diagonal spaces are pairwise isometrically isomorphic.

Tensor diagonals form 1-unconditional basic sequences.

Results apply to n-fold injective and symmetric tensor products.

Abstract

In this paper, we show that four main diagonal spaces of injective tensor products are pairwise isometrically isomorphic. When E is a Banach lattice, we show that the tensor diagonal of E is a 1-unconditional basic sequence in both the n-fold injective tensor product of E and the n-fold symmetric injective tensor product of E.