EXPANDING THE JOINT SPECTRUM OF PAIRS OF COMMUTING CONTRACTIONS

We present a connection between solving the invariant subspace problem for a single operator T on Hilbert space and the existence of a commo n invariant subspace for two commuting related operators. In particula r, we reduce the problem of the existence of nontrivial invariant subs paces for a single contraction with spectral radius one to the problem of the existence of common nontrivial invariant subspaces for a pair of commuting contractions with large joint spectra.