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In this paper we consider those involutions $\theta$ of a finite-dimensionalKac-Moody Lie superalgebra $\mathfrak g$, with associated decomposition$\mathfrak g=\mathfrak k\oplus\mathfrak p$, for which a Cartan subspace$\mathfrak a$ in $\mathfrak p_{\bar 0}$ is self-centralizing in $\mathfrak p$.For such $\theta$ the restriction map $C_\theta$ from $\mathfrak p$ to$\mathfrak a$ is injective on the algebra $P(\mathfrak p)^{\mathfrak k}$ of$\mathfrak k$-invariant polynomials on $\mathfrak p$. There are five infinitefamilies and five exceptional cases of such involutions, and for each case weexplicitly determine the structure of $P(\mathfrak p)^{\mathfrak k}$ by givinga complete set of generators for the image of $C_\theta$. We also determineprecisely when the restriction map $R_\theta$ from $P(\mathfrak g)^{\mathfrakg}$ to $P(\mathfrak p)^{\mathfrak k}$ is surjective. Finally we introduce thenotion of a generalized restricted root system, and show that in the presentsetting the $\mathfrak a$-roots $\Delta(\mathfrak a,\mathfrak g)$ always formsuch a system.

Restriction Theorems and Root Systems for Symmetric Superspaces