phi-semi contractible
Abstract
In this paper, we introduce and investigate the notion of phi-semi contractibility for Banach algebras. We establish a complete characterization of phi-semi contractibility through the existence of specific elements satisfying particular algebraic conditions. We thoroughly examine the hereditary properties of this concept, including its behavior under closed ideals, continuous homomorphisms with dense range, and projective tensor products. Notably, we prove that the projective tensor product A tensor B is phi tensor psi-semi contractible precisely when both A and B are semi contractible with respect to their respective characters, where phi belongs to the character space of A and psi belongs to the character space of B. Furthermore, we introduce and analyze the approximate version of phi-semi contractibility, providing equivalent characterizations.
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BibTeX
@misc{sadeghi2026phisemi,
title = {{phi-semi contractible}},
author = {Hamid Sadeghi and Ali Ghafarpanah},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34434},
eprint = {2609.34434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34434},
}
RIS
TY - UNPB
TI - phi-semi contractible
AU - Hamid Sadeghi
AU - Ali Ghafarpanah
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34434
UR - https://arxiv.org/abs/2609.34434
AB - In this paper, we introduce and investigate the notion of phi-semi contractibility for Banach algebras. We establish a complete characterization of phi-semi contractibility through the existence of specific elements satisfying particular algebraic conditions. We thoroughly examine the hereditary properties of this concept, including its behavior under closed ideals, continuous homomorphisms with dense range, and projective tensor products. Notably, we prove that the projective tensor product A tensor B is phi tensor psi-semi contractible precisely when both A and B are semi contractible with respect to their respective characters, where phi belongs to the character space of A and psi belongs to the character space of B. Furthermore, we introduce and analyze the approximate version of phi-semi contractibility, providing equivalent characterizations.
ER -