Bing Ren LI
We study real operator algebras on a complex Hilbert space H. From H, we can get a real Hilbert space Hr. Further, we have a complex Hilbert space Hrc=Hr iHr. Through this process, we prove the following. If A and M are uniformly closed and weakly closed real * operator algebras on H respectively, then their complex span A+iA and M+iM are (complex) C*-algebra and (complex) von Neumann algebra on H, respectively. Here, we don't need the condition: A∩iA={0}, M∩iM={0}. So our result is a generalization of Stormer's result.