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Suppose [image omitted] is a field with proper involution and of arbitrary characteristic. Additive maps, which do not increase rank-one on hermitian matrices with entries from [image omitted] are classified. The result is then used to classify additive maps that do not increase minimal rank on the set of symmetric elements, relative to general involution on a matrix algebra. [ABSTRACT FROM AUTHOR]

Abstract: Additive mappings, which do not increase the minimal rank of symmetric matrices are classified in characteristic two or three. [Copyright &y& Elsevier]

Additive mappings, which do not increase the minimal rank of alternate matrices, are completely classified. No condition is imposed on the underlying field. [ABSTRACT FROM AUTHOR]

Abstract: Additive bijections , which compress the spectrum between two unital, standard operator algebras, are characterized. Applications to local approximate (anti)multiplications are also given. [Copyright &y& Elsevier]

Let A be a local matrix algebra over a field of characteristic different from 2, B an arbitrary algebra, and X,Y Banach spaces. Additive mappings Φ:A→B, which preserve idempotents are characterized. The result is then used in classifying additive surjections Φ:B(X)→B(Y), which preserve idempotents and do not annihilate finite-rank operators. [Copyright &y& Elsevier]