摘要
In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic to L_r~∞([0,1]) (all real functions in L~∞ ([0, 1])), or L~∞([0, 1])(as a real W~*-algebra), or L_r~∞([0,1]) L_∞([0, 1]) (as a real W~*-algebra), and it is different from the complex case.
In this paper, we point out that most results on abelian (complex) W~*-algebras hold in the real case. Of course, there are differences in homeomorphisms of period 2. Moreover, an abelian real Von Neumann algebra not containing any minimal projection on a separable real Hilbert space is * isomorphic to L_r~∞([0,1]) (all real functions in L~∞ ([0, 1])), or L~∞([0, 1])(as a real W~*-algebra), or L_r~∞([0,1]) L_∞([0, 1]) (as a real W~*-algebra), and it is different from the complex case.
基金
the NNSF
