Abstract:Let $H^{2}$ be the Hardy space over the bidisk. It is known that Hilbert–Schmidt invariant subspaces of $H^{2}$ have nice properties. An invariant subspace which is unitarily equivalent to some invariant subspace whose continuous spectrum does not coincide with $\overline{\mathbb{D}}$ is Hilbert–Schmidt. We shall introduce the concept of splittingness for invariant subspaces and prove that they are Hilbert–Schmidt.
“…Hilbert-Schmidt submodules have many good properties and have been studied extensively in the literature, see e.g. [8,[16][17][18][19] and the references therein. In particular, it was shown in [19] that C 2 is unitarily equivalent to…”
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