Krein–Rutman theorem

In functional analysis, the Krein–Rutman theorem is a generalisation of the Perron–Frobenius theorem to infinite-dimensional Banach spaces.[1] It was proved by Krein and Rutman in 1948.be a convex cone such that, i.e. the closure of the setis also known as a total cone.be a non-zero compact operator, and assume that it is positive, meaning that, and that its spectral radiuswith positive eigenvector, meaning that there exists, then de Pagter's theorem[3] asserts thatTherefore, for ideal irreducible operators the assumption

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