Abstract

This paper is concerned with spectral properties of an integral operator with a nonnegative continous kernel. Various conditions are given for the existence of a positive eigenvalue of maximum modulus, its simplicity, and the existence of a corresponding positive eigenfunction. Other results describe the distribution of secondary eigenvalues. The operators considered include those with stochastic kernels and those with irreducible kernels. In addition to new results, simple new proofs are given for fundamental properties of operators with positive kernels. The analysis involves collectively compact operator approximation theory, transpose operators, the spectral mapping theorem, and an extremal characterization of the spectral radius.

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