A system of orthogonal projections in generic position generates a C*-algebra closely related to the one generated by Toeplitz operators with vertical symbols on poly-Bergman spaces of the upper half-plane.
Glimm, A Stone-Weierstrass theorem for C^* -algebras , Annals of Mathematics 72 , 1 (1960) 216--244
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On a relationship between orthogonal projections and Toeplitz operators on poly-Bergman spaces of the upper half-plane: vertical symbols
A system of orthogonal projections in generic position generates a C*-algebra closely related to the one generated by Toeplitz operators with vertical symbols on poly-Bergman spaces of the upper half-plane.