We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra is acting irreducibl...We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.展开更多
In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernel...In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernels are discussed.展开更多
Let A be a separable simple C*-algebra. For each a(≠0) in A, there exists a separable faithful and irreducible * representation (π, Hπ) on A such that π(a) has a non-trivial invariant subspace in Hπ.
文摘We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.
基金Partially supported by the National Natural Science Foundation of China.
文摘In this paper,we show that a topologically irreducible * representation of a real C~*- algebra is also algebraically irreducible.Moreover,the properties of pure real states on a real C~*- algebra and their left kernels are discussed.
基金the NSF of Beijing (1022004)the Foundation of organization depart ment in Beijing Municipal Party CommitteeDoctorial Science Foundation of North China Electric Power University
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10101026).
文摘Let A be a separable simple C*-algebra. For each a(≠0) in A, there exists a separable faithful and irreducible * representation (π, Hπ) on A such that π(a) has a non-trivial invariant subspace in Hπ.