Lattice properties of the core-partial order
MS Djikić - 2017 - projecteuclid.org
2017•projecteuclid.org
We show that in an arbitrary Hilbert space, the set of group-invertible operators with respect
to the core-partial order has the complete lower semilattice structure, meaning that an
arbitrary family of operators possesses the core-infimum. We also give a necessary and
sufficient condition for the existence of the core-supremum of an arbitrary family, and we
study the properties of these lattice operations on pairs of operators.
to the core-partial order has the complete lower semilattice structure, meaning that an
arbitrary family of operators possesses the core-infimum. We also give a necessary and
sufficient condition for the existence of the core-supremum of an arbitrary family, and we
study the properties of these lattice operations on pairs of operators.
Abstract
We show that in an arbitrary Hilbert space, the set of group-invertible operators with respect to the core-partial order has the complete lower semilattice structure, meaning that an arbitrary family of operators possesses the core-infimum. We also give a necessary and sufficient condition for the existence of the core-supremum of an arbitrary family, and we study the properties of these lattice operations on pairs of operators.
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