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arXiv · 1805.06574

A canonical decomposition of strong $L^2$-functions

In Sung Hwang·Woo Young Lee
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Abstract

The aim of this paper is to establish a canonical decomposition of operator-valued strong $L^2$-functions by the aid of the Beurling-Lax-Halmos Theorem which characterizes the shift-invariant subspaces of vector-valued Hardy space. This decomposition invites us to coin a new notion of the "Beurling degree" of the inner function. Eventually, we establish a deep connection between the spectral multiplicity of the model operator and the Beurling degree of the corresponding characteristic function.

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In Sung Hwang, Woo Young Lee. 2019-10-23. A canonical decomposition of strong $L^2$-functions. https://arxiv.org/abs/1805.06574

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