he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure ${}_{\beta }$, via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure ${}_{\beta }$ by using the so-called β-type Wick product.

We introduce various classes of interpolation sets for Fréchet measures-the measure-theoretic analogues of bounded multilinear forms on products of C(K) spaces.

The invariant subspace problem for some operators and some operator algebras acting on a locally convex space is studied.

It is proved, using so-called multirectangular invariants, that the condition αβ = α̃β̃ is sufficient for the isomorphism of the spaces $E₀\left(exp\alpha i\right)\otimes ̂E_{\infty }\left(exp\beta j\right)$ and $E₀\left(exp\alpha ̃i\right)\otimes ̂E_{\infty }\left(exp\beta ̃j\right)$. This solves a problem posed in [14, 15, 1]. Notice that the necessity has been proved earlier in [14].