If H is a Hilbert space, S ⊆ H is a closed subspace of H, and A is a positive bounded linear operator on H, the spectral shorted operator ρ(S, A) is defined as the infimum of the sequence Σ(S, An ) 1/n, where Σ(S, B) denotes the shorted operator of B to S. We characterize the left spectral resolution of ρ(S, A) and show several properties of this operator, particularly in the case that dim S = 1. We use these results to generalize the concept of Kolmogorov complexity for the infinite dimesional case and for non invertible operators.Facultad de Ciencias Exactas