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Journal Article

# THE CENTRALIZER UNDER TENSOR PRODUCT

RICHARD H. HERMAN
Mathematica Scandinavica
Vol. 36, No. 2 (September 19, 1975), pp. 286-290
Stable URL: http://www.jstor.org/stable/24491134
Page Count: 5

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Topics: Von Neumann algebra, Automorphisms, Tensors, Mathematical theorems, Eigenvalues

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Let Mφ denote the fixed points of the modular automorphism group $\mathrm{t}\to {\mathrm{\sigma }}_{\mathrm{t}}^{\mathrm{\phi }}$ of a faithful, normal state, φ, on a von Neumann algebra M. We calculate $(\mathrm{M}\overline{\otimes }\mathrm{N}{)}_{\mathrm{\phi }\otimes \mathrm{\psi }}$ when φ and ψ are periodic. In general we show when $(\mathrm{M}\overline{\otimes }\mathrm{N}{)}_{\mathrm{\phi }\otimes \mathrm{\psi }}={\mathrm{M}}_{\mathrm{\phi }}\overline{\otimes }{\mathrm{N}}_{\mathrm{\phi }}$. We also give a discussion of eigenoperators for a modular automorphism group.