Abstract
Let M n be the set of n × n complex matrices, and for ε > 0 and A ∈ M n , let σ ε ( A ) denote the ε − pseudo spectrum of A. Maps Φ on M n which preserve the skew Lie product of matrices in a sense that σ ε ( Φ ( A ) Φ ( B ) − Φ ( B ) Φ ( A ) ∗ ) = σ ε ( AB − B A ∗ ) ( A , B ∈ M n ) are characterized, with no surjectivity assumption on them. Analogous description for the skew product on matrices is also noted.
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