The Pair Of Mappable Pairs On The Triangular Algebra And The Lie-guided Map Pair

The maps of operator algebra have close connection with intrinsic properties of operator algebra. In order to discuss the structure of operator algebra, many scholars have researched additive or linear mapping on operator algebra. Recently, the maps without additivity and linearity assumping have aroused concern. On the basis of existing papers, in this paper, we mainly study three pairs of rnaps(without additivity and linearity assumping),that is the pairs of derivable maps, the pairs of Jordan derivable maps, and the pairs of Lie derivable maps on triangular algebras The details are as follows:In Chapter 1, we give some common symbols and definitions. For example, triangular algebras, derivable maps, the pairs of derivable maps, the pairs of Jordan derivable maps, the pairs of Lie derivable maps and so on.In Chapter 2, we mainly discuss the additivity of the pairs of derivable maps on triangular algebras, we prove that the pairs of derivable maps on triangular algebras are additive, and we obtain them concrete structure, if (?, ?) is the pairs of derivable maps on it, that is ?(ab)= ?(a)b+a?(b), then ?,? is additive and ? is a generalized derivation with ? is the relating derivation.In Chapter 3, we mainly study the pairs of Jordan derivable maps on triangular algebras, we prove that the pairs of Jordan derivable maps is additive, and obtain the concrete structure of them, if (?, ?) is the pairs of Jordan derivable maps on it, that is ?(a o b)= ? (a) o b+a o ?(b),, then ?, ? is additive and and is the pairs of derivable maps on triangular algebras.In Chapter 4, we give that the concrete form of the pairs of Lie derivable maps on triangular algebras when it satisfies some conditions, we obtain that if (?, ?) is the pairs of Lie derivable maps on it, then ? is the sum of an additive generalized derivation and a central-value map, and ? is the sum of an additive derivation and a central-value map.