2025/03/18 by Yicao, Wang
#47A20 #47A45 #47A67 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2503.13977
The paper presents a new functional model for completely non-unitary contractions on a Hilbert space. This model is based on the observation that the theory of contractions shares a common geometric basis with the extension theory of symmetric operators recently developed by the author in \citewang2024complex. Compared with the now classical Sz.-Nagy-Foias model and the de Branges-Rovnyak model, ours is intrinsic in the sense that we need not construct a bigger space H including the model space \mathfrakH and realize the model operator on \mathfrakH as the compression of a minimal unitary dilation on H. Our model space \mathfrakH is constructed in a canonical and conceptually more direct manner and doesn't depend on the Sz. Nagy-Foias characteristic function explicitly. We also show how a contraction can be constructed from a marked Nevanlinna disc, which is the geometric analogue of the characteristic function.