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Doubly Stochastic Matrices
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absolutely summing adjoint AM-space Archimedean Banach lattice Banach space band projection Boolean algebra called canonical order Chap closed ideal closed vector sublattice compact space complete vector lattice complex vector contains continuous linear forms Corollary countably countably order complete cyclic defined denote dimensional dual eigenvalue Example Exerc exists extreme point finite follows hence Hilbert hypothesis identified IM-space with unit implies integral irreducible lattice homomorphism Lemma locally compact space m-norm matrix maximal ideal mean ergodic measure space minimal modulus Moreover non-void normed vector lattice null sequence operator norm order continuous norm order interval permutation matrix positive linear form positive operators projection band Proof Proposition quasi-interior positive elements Radon measure representation space respectively S-ideal satisfying semi-group spectral radius stochastic strictly positive subset Suppose theorem theory topological vector topology unit ball vector space vector subspace weak order unit weakly compact