The Study Of Complex F-Algebra And Orthomorphism

In this paper, the elementary concepts of complex Riesz space and complex f -algebra are introduced first. Based on the knowledge of real f -algebra, the important properties of semi and unital complex f -algebra are studied. On the condition of normality, the question whether the unital complex f -algebra satisfies the (*) property and multiple decomposition property are considered. Moreover the relationship between order ideal and algebra ideal in complex f -algebra are discussed in great details.Complex Riesz homomorphism is a kind of interesting operator. The algebra homomorphism and Riesz homomorphism can be deducible for each other under some circumstances in complex f -algebra. And the generalized Schwarz inequality for complex Riesz homomorphism is obtained as well as some useful corollaries.Finally, complex orthomorphism which is intimate with complex f -algebra is fully studied. The construction of complex orthomorphism is created, and based on it the connection of complex f -algebra and complex orthomorphism is discussed. Meanwhile some unsolved questions in complex f -algebra are worked out. In addition, the proposition that every range of complex orthomorphism is an order ideal is concluded when real Riesz space is normal.