Kadison's theorem is proved for countable weak-operator compact sets of bounded self-adjoint operators, and results on maximal lower bounds and greatest positive lower bounds are generalized to finite sets of positive matrices and commuting operators.
Stott,Maximal lower bounds in the Löwner order, 2016,arXiv:1612.05664 [math.RA]
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Remarks on infimum and maximal lower bounds of a set of bounded self-adjoint operators
Kadison's theorem is proved for countable weak-operator compact sets of bounded self-adjoint operators, and results on maximal lower bounds and greatest positive lower bounds are generalized to finite sets of positive matrices and commuting operators.