Annihilating ideals and Agler--McCarthy spectral varieties in the bidisc

Raphaël Clouâtre, Poornendu Kumar

The closed unit bidisc ${\overline{\mathbb{D}}}^2$ is known to be a spectral set for any pair $(T_1,T_2)$ of commuting contractions. When each $T_i$ is pure and has finite defect, th…