Abstract
The purpose of this note is to consider the lattice properties of (the set of all idempotent operators on a Hilbert space ) with respect to the star partial order. In the domain of we prove that the star infimum always exists for an arbitrary nonempty subset of . Also, we present the necessary and sufficient conditions for the existence of the star supremum for an arbitrary nonempty subset of . In particular, an explicit representation of the star supremum is established for two arbitrary idempotent operators in .
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