Weyl's theorems and Kato spectrum.
Weyl's type theorems and perturbations.
Wold-type extension for N-tuples of commuting contractions
Let (T1,…,TN) be an N-tuple of commuting contractions on a separable, complex, infinite-dimensional Hilbert space ℋ. We obtain the existence of a commuting N-tuple (V1,…,VN) of contractions on a superspace K of ℋ such that each extends , j=1,…,N, and the N-tuple (V1,…,VN) has a decomposition similar to the Wold-von Neumann decomposition for coisometries (although the need not be coisometries). As an application, we obtain a new proof of a result of Słociński (see [9])