PreprintCC BY 4.0arXiv
Explicity Defined Norms on JT* Spaces
Abstract
We present a Banach space Xα, equipped with an explicit norm, whose properties resemble those of the predual JT* of the James Tree space. In particular, Xα admits a shrinking dyadic basis with the property that the sums of its elements over any segment are uniformly bounded. The space Xα is complementably ℓ2-saturated, and its dual Xα* does not contain an isomorphic copy of ℓ1. Finally, the bidual Xα** is also complementably ℓ2-saturated, and the quotient Xα**/Xα is isometric to c0(2ℕ).
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BibTeX
@misc{argyros2026explicity,
title = {{Explicity Defined Norms on $JT_*$ Spaces}},
author = {Spiros A. Argyros and Pavlos Motakis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31276},
eprint = {2609.31276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31276},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explicity Defined Norms on JT_* Spaces
AU - Spiros A. Argyros
AU - Pavlos Motakis
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31276
UR - https://arxiv.org/abs/2609.31276
AB - We present a Banach space X_α, equipped with an explicit norm, whose properties resemble those of the predual JT_* of the James Tree space. In particular, X_α admits a shrinking dyadic basis with the property that the sums of its elements over any segment are uniformly bounded. The space X_α is complementably ℓ_2-saturated, and its dual X_α^* does not contain an isomorphic copy of ℓ_1. Finally, the bidual X_α^** is also complementably ℓ_2-saturated, and the quotient X_α^**/X_α is isometric to c_0(2^ℕ).
ER -