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.
Citation
Marko S. Djikić. "Lattice properties of the core-partial order." Banach J. Math. Anal. 11 (2) 398 - 415, April 2017. https://doi.org/10.1215/17358787-0000010X
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