This is a review of a coherent body of knowledge, which perhaps
deserves the name of the geometric spectral theory of positive linear operators
(in finite dimensions), developed by this author and his co-author Hans
Schneider (or S.F. Wu) over the past decade. The following topics are covered,
besides others: combinatorial spectral theory of nonnegative matrices,
Collatz-Wielandt sets (or numbers) associated with a cone-preserving map,
distinguished eigenvalues, cone-solvability theorems, the peripheral spectrum
and the core, the invariant faces, the spectral pairs, and an extension of the
Rothblum Index Theorem. Some new insights, alternative proofs, extensions
or applications of known results are given. Several new results are proved or
announced, and some open problems are also mentioned.
關聯:
臺灣數學期刊=Taiwanese Journal of Mathematics 5(2), pp.207-277
