Polynomial extension property in the classical Cartan domain $${\mathcal {R}_{II}}$$

In this work, it is shown that for the classical Cartan domain $$\mathcal {R}_{II}$$ R II consisting of symmetric $$2\times 2$$ 2 × 2 matrices, every algebraic subset of $$\mathcal {R}_{II}$$ R II , which admits the polynomial extension property, is a holomorphic retract.

INTERSECTIONS OF HOLOMORPHIC RETRACTS IN BANACH SPACES

Using the Kobayashi distance, we provide sufficient conditions for the intersection of a family of holomorphic retracts in a Banach space to also be a holomorphic retract.