PreprintCC BY 4.0arXiv
The convolution product is generally not an open map
Abstract
We show that the convolution product ℓ1(G)× ℓ1(G)→ ℓ1(G) is not an open map if G is either non-abelian or contains an element of infinite order. The case G=ℤ solves a problem posed by Kania and Maślany.
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BibTeX
@misc{flores2026convolution,
title = {{The convolution product is generally not an open map}},
author = {Felipe I. Flores},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38722},
eprint = {2610.38722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38722},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The convolution product is generally not an open map
AU - Felipe I. Flores
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38722
UR - https://arxiv.org/abs/2610.38722
AB - We show that the convolution product ℓ^1(G)× ℓ^1(G)→ ℓ^1(G) is not an open map if G is either non-abelian or contains an element of infinite order. The case G=ℤ solves a problem posed by Kania and Maślany.
ER -