PreprintCC BY 4.0arXiv
The Separable Quotient Problem and the Lotz Property in Banach Spaces
Abstract
In this paper, in addition to establishing several new sufficient or equivalent conditions for the well-known Separable Quotient Problem (SQP), we show that every infinite-dimensional Banach space lacking the Lotz property admits a separable quotient, thereby revealing a surprising connection between the SQP and semigroup theory.
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BibTeX
@misc{araujo2026separable,
title = {{The Separable Quotient Problem and the Lotz Property in Banach Spaces}},
author = {Gustavo Araújo and Anderson Barbosa and Juan B. Seoane-Sepúlveda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00584},
eprint = {2610.00584},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00584},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Separable Quotient Problem and the Lotz Property in Banach Spaces
AU - Gustavo Araújo
AU - Anderson Barbosa
AU - Juan B. Seoane-Sepúlveda
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00584
UR - https://arxiv.org/abs/2610.00584
AB - In this paper, in addition to establishing several new sufficient or equivalent conditions for the well-known Separable Quotient Problem (SQP), we show that every infinite-dimensional Banach space lacking the Lotz property admits a separable quotient, thereby revealing a surprising connection between the SQP and semigroup theory.
ER -