2025/10/28 by Konstantos, Konstantinos, Motakis, Pavlos
#46B09 #46B25 #46B28 #46E30 #47A68 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2510.24487
For every 1≤ α<ω1, we construct an explicit unconditional finite-dimensional decomposition (FDD) (Xλ)λ\inTα of the Bourgain-Rosenthal-Schechtman space Rαp,0 by blocking its standard martingale difference sequence (MDS) basis. This FDD has strong reproducing properties and supports a theory of distributional representations between the spaces Rαp,0, 1≤ α<ω1. We use this framework to prove an approximate orthogonal reduction: every bounded linear operator on a limit space Rαp,0 is, via a distributional embedding and up to arbitrary precision, reduced to a scalar FDD-diagonal operator. As a consequence, the standard MDS bases of the limit spaces Rαp,0 satisfy the factorization property.