2018/01/23 by Eschmeier, Jörg, Langendörfer, Sebastian · 1 citation
#47A13 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1801.07520
Let Hm(\mathbb B) be the analytic functional Hilbert space on the unit ball \mathbb B ⊂ \mathbb Cn with reproducing kernel Km(z,w) = (1 - ⟨ z,w ⟩)-m. Using algebraic operator identities we characterize those commuting row contractions T ∈ L(H)n on a Hilbert space H that decompose into the direct sum of a spherical coisometry and copies of the multiplication tuple Mz ∈ L(Hm(\mathbb B))n. For m=1, this leads to a Wold decomposition for partially isometric commuting row contractions that are regular at z = 0. For m = 1 = n, the results reduce to the classical Wold decomposition of isometries. We thus extend corresponding one-variable results of Giselsson and Olofsson to the case of the unit ball.