Noncommutative Calderón-Lozanovskiĭ-Hardy spaces
Let \(\mathcal M\) be a von Neumann algebra with a faithful normal semi-finite trace \(\tau\) and let $E$ be a symmetric quasi-Banach space. For any Orlicz function \(\varphi\), we can define the noncommutative Calderón-Lozanovskiĭ spaces \(E_{\varphi}(\mathcal M)\). In the present paper, the authors give several properties of those spaces similar to those of their classical counterparts. Specifically, by introducing a noncommutative Calderón-Lozanovskiĭ space \(E_{\varphi}(\mathcal M)\), the authors give the multiplication operator space and the complex interpolation on \(E_{\varphi}(\mathcal M)\). Furthermore, based on a semi-finite subdiagonal algebra \(\mathcal A\) with respect to a faithful normal expectation \(\mathcal E\) such that \(\tau\circ\mathcal E=\tau\) in \(\mathcal M\), the authors introduce a noncommutative Calderón-Lozanovskiĭ-Hardy space \(H^{\varphi}(\mathcal A)\) and transfer the recent results of the noncommutative Hardy space to this version. For example, certain complex interpolation theorems as well as factorization theorems are obtained. At last, a new version of Beurling's theorem for \(\mathcal A\)-invariant subspaces in noncommutative Calderón-Lozanovskiĭ-Hardy spaces is proved.
noncommutative Calderón-Lozanovskiĭ spaces
scientific article; zbMATH DE number 7345586
scientific article