A non-unital algebra has UUNP iff its unitization has UUNP
classification
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uunpalgebranon-unitalunitizationbanachbhattdedaniahere
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Let $A$ be a non-unital Banach algebra, S. J. Bhatt and H. V. Dedania showed that $A$ has the unique uniform norm property (UUNP) if and only if its unitization has UUNP. Here we prove this result for any non-unital algebra.
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