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- W4387295779 abstract "Tomita-Takesaki theory associates a positive operator called the modular operator with a von Neumann algebra and a cyclic-separating vector. Tomita's theorem says that the unitary flow generated by the modular operator leaves the algebra invariant. I give a new, short proof of this theorem which only uses the analytic structure of unitary flows, and which avoids operator-valued Fourier transforms (as in van Daele's proof) and operator-valued Mellin transforms (as in Zsid'{o}'s and Woronowicz's proofs). The proof is similar to one given by Bratteli and Robinson in the special case that the modular operator is bounded." @default.
- W4387295779 created "2023-10-04" @default.
- W4387295779 creator A5071821544 @default.
- W4387295779 date "2023-09-28" @default.
- W4387295779 modified "2023-10-04" @default.
- W4387295779 title "A short proof of Tomita's theorem" @default.
- W4387295779 doi "https://doi.org/10.48550/arxiv.2309.16762" @default.
- W4387295779 hasPublicationYear "2023" @default.
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