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Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.

2 votes
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Perron-Frobenius theory for operators on matrices

Let $A$ be a Hermitian linear operator on the space of $n\times n$ complex matrices. Let's suppose $A$ is "non-negative" in the sense that it preserves the cone of non-negative definite (Hermitian) ma …