发表机构
Islamic Azad University; Salman Farsi University of Kazerun（伊斯兰阿扎德大学; 卡泽伦萨曼法尔西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入Banach代数的phi-半可收缩性概念，给出其完整刻画，研究遗传性质，并证明射影张量积的等价条件，同时分析近似版本。
AI 中文摘要
本文引入并研究了Banach代数的phi-半可收缩性概念。我们通过存在满足特定代数条件的特定元素，建立了phi-半可收缩性的完整刻画。我们深入考察了该概念的遗传性质，包括其在闭理想、具有稠密值域的连续同态以及射影张量积下的行为。值得注意的是，我们证明了射影张量积A⊗B是phi⊗psi-半可收缩的，当且仅当A和B分别关于其各自的特征是半可收缩的，其中phi属于A的特征空间，psi属于B的特征空间。此外，我们引入并分析了phi-半可收缩性的近似版本，并给出了等价刻画。
英文摘要
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.
