Cones and Gauges in Complex Spaces : Spectral Gaps and Complex Perron-frobenius Theory

@inproceedings{RughConesAG,
  title={Cones and Gauges in Complex Spaces : Spectral Gaps and Complex Perron-frobenius Theory},
  author={Hans Henrik Rugh}
}
We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated complex cone-contraction Theorem and use it to extend the classical Perron-Frobenius Theorem to complex matrices, Jentzsch's Theorem to complex integral operators, a Kre˘ ın-Rutman Theorem to compact and quasi-compact complex operators and a Ruelle-Perron… CONTINUE READING

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