Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Sadeghi, Hamid, Ghafarpanah, Ali
Institution: Salman Farsi University of Kazerun
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214719952