Mathematica Eterna
Open Access

Abstract

On the Riesz Space Decomposition Theorem

Junfeng Liu

In this paper, we extend the famous Jordan Space Decomposition Theorem and Riesz Space Decomposition Theorem, and the proof of the result of this paper does not depend on two theorems above. Since Jordan′ s Theorem and Riesz′ s Theorem are two famous results in operator theory, the two theorems are often detailed in the same book. Using the result of this paper, one may modify the discussion of the Riesz′ s Theorem, and omit the discussion of Jordan′ s Theorem, then two theorems above are obtained as corollaries.