Character Injectivity And Projectivity Of Banach Modules
Rasoul Nasr-Isfahani
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Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
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School of Mathematics, Institute for Research in Fundamental Science (IPM), Tehran, P.O. Box: 19395-5746, Iran
Sima Soltani Renani
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Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
Abstract
Let A be a Banach algebra and let φ be a non-zero character on A. We introduce and study the notions φ-injectivity and φ-projectivity for Banach A-modules ℰ by modifying the injectivity and projectivity of ℰ. We give some necessary and sufficient conditions for φ-injectivity and φ-projectivity of ℰ. In sequel, we establish an important relationship between φ-amenability of A and φ-injectivity of ℰ. This gives a positive answer to a question of Hellemskii in the setting of injectivity based on φ.