{'fraction_non_alphanumeric': 0.015317286652078774, 'fraction_numerical': 0.00437636761487965, 'mean_word_length': 5.026315789473684, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Invariant subspaces for H2 spaces of σ ‐finite algebras

We show that a Beurling type theory of invariant subspaces of noncommutative H2 spaces holds true in the setting of subdiagonal subalgebras of σ ‐finite von Neumann algebras. This extends earlier work by Blecher and Labuschagne on finite algebras, and complements more recent contributions in this regard by Bekjan and Chen, Hadwin and Shen in the finite setting, and Sager in the semifinite setting.