PreprintCC BY-NC 4.0HAL
Interpolation of subspaces of infinite codimension
Abstract
Given three normed spaces X0 , X1 , X1̃, with X1̃ a closed subspace of X1 with same norm, how does [X0 , X1 ]θ compare to $[X_0 , X_1 ]_\theta ? This classical problem of interpolation theory has been mostly considered in the case of finite codimensional subspaces. We show here that quotient J norms are a useful tool which allows to tackle several relevant cases.
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BibTeX
@misc{audiard2026interpolation,
title = {{Interpolation of subspaces of infinite codimension}},
author = {Corentin Audiard},
howpublished = {HAL},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2609.26519},
eprint = {2609.26519},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05757375v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Interpolation of subspaces of infinite codimension
AU - Corentin Audiard
PY - 2026
DA - 2026/08/03
PB - HAL
DO - 10.48550/arxiv.2609.26519
UR - https://hal.science/hal-05757375v1
AB - Given three normed spaces X_0 , X_1 , X_1̃, with X_1̃ a closed subspace of X_1 with same norm, how does [X_0 , X_1 ]_θ compare to $[X_0 , X_1 ]_\theta ? This classical problem of interpolation theory has been mostly considered in the case of finite codimensional subspaces. We show here that quotient J norms are a useful tool which allows to tackle several relevant cases.
ER -