Ordinal indices for complemented subspaces of l_p
S. Dutta, D. Khurana
TL;DR
This paper investigates the invariance properties of complemented subspaces of L_p, computes their ordinal indices, and establishes a dichotomy based on these indices, advancing understanding of their structure.
Contribution
It introduces the complete isomorphic invariance of certain complemented subspaces of L_p and computes their ordinal indices, providing new insights into their classification.
Findings
Complete isomorphic invariance of a class of subspaces
Calculation of ordinal L_p-indices for these subspaces
A dichotomy for subspaces with small ordinal indices
Abstract
We provide complete isomorphic invariance of a class of translation invariant complemented subspaces of L_p constructed by Bourgain, Rosenthal and Schechtman. We compute ordinal L_p-indices for this class. We further show that the isometric index of a tree subspace over a well founded tree is an invariance for the order of the tree. Finally we provide a dichotomy for the subspaces of L_p with small ordinal indices.
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Taxonomy
TopicsGraph theory and applications · Markov Chains and Monte Carlo Methods · Topological and Geometric Data Analysis