Abstract
We characterize surjective linear maps that preserve the minimum modulus between unital semisimple Banach algebras, one of them is a unital C ∗ -algebra having either real rank zero or essential socle. We also describe surjective linear maps on L(H), with H an infinite- dimensional Hilbert space, preserving the essential minimum modulus. Results concerning sur- jectivity and maximum modulus are also obtained.
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