The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions d...The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions does a inherit that property？ This will be referred to as the domination problem. In this paper we will introduce absolute value ｜.｜ in an OBA and obtain results for the domination problem under the more general inequality ｜α｜ ≤｜b｜. We will show that these results are applicable to positive operators on a Banach lattice. Furthermore, it will be demonstrated that some known results for the domination problem in OBAs continue to hold true if 0 ≤ α≤ b is replaced by ｜a｜≤｜b｜.展开更多
文摘The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions does a inherit that property？ This will be referred to as the domination problem. In this paper we will introduce absolute value ｜.｜ in an OBA and obtain results for the domination problem under the more general inequality ｜α｜ ≤｜b｜. We will show that these results are applicable to positive operators on a Banach lattice. Furthermore, it will be demonstrated that some known results for the domination problem in OBAs continue to hold true if 0 ≤ α≤ b is replaced by ｜a｜≤｜b｜.
