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Structural properties of close \(\mathrm{II}_1\) factors. (English) Zbl 1379.46045

Summary: We show a number of key structural properties transfer between sufficiently close \(\mathrm{II}_1\) factors, including solidity, strong solidity, uniqueness of Cartan masas and property \(\Gamma\). We also examine \(\mathrm{II}_1\) factors close to tensor product factors, showing that such factors also factorize as a tensor product in a fashion close to the original.

MSC:

46L10 General theory of von Neumann algebras
46L36 Classification of factors
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