Abstract
The lattice of closed right ideals is an important invariant of a C*-algebra and naturally generalizes the spectrum of a commutative C*-algebra. As the C*-algebra is a union of its commutative sub-C*-algebras, the lattice can be considered as a “piecewise frame”. It is discussed here that there is no right residuated total operation extending the meet operation on compatible elements, no “Sasakian” product, and no active lattice structure.
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