Let $G/K$ be a Hermitian symmetric space of non-compact type. We consider for the so-called minimal Olshanskii semigroup $\Gamma\subset G^C$, the C$^*$-algebra $T$ generated by all Toeplitz operators $T_f$ on the Hardy space $H^2(\Gamma)\subset L^2(G)$. We describe the construction of ideals of $T$ associated to boundary strata of the domain $\Gamma$.
Invariant coneAlgebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)Hermitian symmetric spaceJordan triple systemToeplitz algebraHardyy space
