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Let $A$ be a non unital Banach algebra. The product induces a bounded linear map $T:A \otimes_{\gamma} A\to A$ where $\otimes_\gamma$ denotes the Banach projective tensor product. A lifting of $T$ is a bounded linear map $L:A\to A \otimes_{\gamma} A$ such that $TL=Id_{A}$. Do you know a charaterization or examples of algebras which admits a such lifting? Any reference on this problem or explicit examples is welcome. UPDATE: I added non unital. |
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Lifting of product of a Banach algebraLet $A$ be a Banach algebra. The product induces a bounded linear map $T:A \otimes_{\gamma} A\to A$ where $\otimes_\gamma$ denotes the Banach projective tensor product. A lifting of $T$ is a bounded linear map $L:A\to A \otimes_{\gamma} A$ such that $TL=Id_{A}$. Do you know a charaterization or examples of algebras which admits a such lifting? Any reference on this problem or explicit examples is welcome.
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