. "A."@en . "InternetArchiveBot"@en . . . "Shtern"@en . "2018-05-07T18:45:45Z"^^ . "yes"@en . "Minoru Tomita"@en . "T/t120150"@en . . "Takesaki"@en . "Hilbert algebra"@en . "A.I."@en . "In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita\u2013Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution."@en . "In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita\u2013Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution. It is essential for the theory of type III factors, and has led to a good structure theory for these previously intractable objects.The theory was introduced by Minoru Tomita (1967), but his work was hard to follow and mostly unpublished, and little notice was taken of it until Masamichi Takesaki (1970) wrote an account of Tomita's theory."@en . "Tomita"@en . . "1967"^^ . "820305606"^^ . . "Tomita\u2013Takesaki theory"@en . "1970"^^ . . . "Minoru"@en . "2898625"^^ . . "2018-01-14T03:18:43Z"^^ . "15"^^ . "Inoue"@en . . . . "2016-08-19T06:44:09Z"^^ . . "Masamichi"@en . . . . . . "H/h047230"@en . . . "January 2018"@en . . "Tomita\u2013Takesaki theory"@en . . "Masamichi Takesaki"@en . . . "9543"^^ . . . . . . .