A Remark on an Infinite Tensor Product of von Neumann Algebras

  • Huzihiro Araki

    Kyoto University, Japan
  • Yoshiomi Nakagami

    Tokyo Institute of Technology, Japan

Abstract

Let be the incomplete infinite tensor product of Hilbert spaces containing a product vector , where denotes the equivalence class of the -sequence . Let be the projection on in the complete infinite tensor product of . Let be the von Neumann algebra on generated by von Neumann algebra on and be the central support of in . Two -sequences and , and their equivalence classes and , are defined to be -equivalent if there exist partial isometries such that and are equivalent and . They are defined to be _-equivalent if can be chosen unitary. We prove that is the sum of with , -equivalent to . If the index set is countable, -equivalence and -equivalence coincide.

Cite this article

Huzihiro Araki, Yoshiomi Nakagami, A Remark on an Infinite Tensor Product of von Neumann Algebras. Publ. Res. Inst. Math. Sci. 8 (1972), no. 2, pp. 363–374

DOI 10.2977/PRIMS/1195193114