Publication: Invariant subspaces for positive operators on Banach spaces with unconditional basis
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2022-06-16
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American Mathematical Society
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We prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on X extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.
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