PreprintarXiv licencearXiv
On Exposed (Symmetric) Tensors
Abstract
We provide an example of a projective tensor product whose unit ball contains an exposed tensor which is not elementary. We then transfer the construction to the symmetric projective tensor product and obtain an analogous result in that setting. Finally, we extend both constructions to projective tensor products with an arbitrary number of factors and to symmetric projective tensor products of every degree.
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BibTeX
@misc{dantas2026exposed,
title = {{On Exposed (Symmetric) Tensors}},
author = {Sheldon Dantas and Martin Mazzitelli and Jorge Tomás Rodríguez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01835},
eprint = {2609.01835},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01835},
}
RIS
TY - UNPB
TI - On Exposed (Symmetric) Tensors
AU - Sheldon Dantas
AU - Martin Mazzitelli
AU - Jorge Tomás Rodríguez
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01835
UR - https://arxiv.org/abs/2609.01835
AB - We provide an example of a projective tensor product whose unit ball contains an exposed tensor which is not elementary. We then transfer the construction to the symmetric projective tensor product and obtain an analogous result in that setting. Finally, we extend both constructions to projective tensor products with an arbitrary number of factors and to symmetric projective tensor products of every degree.
ER -