On common invariant subspaces for commuting contractions with rich spectrum Marek KosiekAlfredo Octavio 47A6047A15contractionsdual algebrasfunctional calculusinvariant subspaces In this paper we show that an $N$-tuple of commuting contractions $T=(T_1,\dots,T_N)$ acting on a separable, complex Hilbert space $\mathcal{H}$ having the polydisk ($\mathbb{D}^N$) as a spectral set and dominating Harte spectrum, has a nontrivial common invariant subspace (i.e., a proper subspace $\{0\}\ne\mathcal{M}\subset\mathcal{H}$, such that $T_j\mathcal{M}\subset\mathcal{M}$ for $j=1$, $\dots$, $N$). We do not need to assume any kind of $C_{0\mbox{$\cdot$}}$ condition for any member of our $N$-tuple. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2221 10.1512/iumj.2004.53.2221 en Indiana Univ. Math. J. 53 (2004) 823 - 844 state-of-the-art mathematics http://iumj.org/access/