On Operator Algebras Mapping

Operator algebra is a important buanch booming quickly of mathematics field in recent years, which fairly support and inhance the development of physics and power. Maps is a inportant tool in linear algebra and play a vital role in the study of characterization of algebra. So the study of maps on algebra has never been droped. This theme devotes to the discuss of maps on some limit algebra and non-self-adjoit algebra. There are four chapters. The main part is from chapter two to chapter four.Chapter one is introduction.In chapter two, firstly I discuss the linear problem of local automorphism on AF C* algebra.The proof of it makes full use of the spascial frame-matrix unit system. Secondly, for the spascial AF C* algebra-UHF algebra, I study the linear characterization of 2-local isometry on it: make use of the frame attribute, find the trace state of UHF algebra according to the one of matrix algebra and verify the 2-local isometry is linear.Recently, more and more people pay attention to the problem from the part to the whole of this kind, which we can see in the reference [5], [6], [7]. Instructed by them, I get the conclutions of this chaper.In chapter three, I study the isometric maps on non-self-adjoit AF C* algebra.. In reference [15], Muhly discribe the isometric algebral isomorphism and isometric reflixive algebra isomorphism on some triangle subalgebra og Nenclear algebra with diagonent. The first problem of this chapter is analyzing furtherlythe concrete form of the isometry on TUHF algebra. Similar to the second conclution of chapter two, I also study the linear characterization of 2-local isometry on TUHF algebra. The way of proof is same.In chapter four, I discribe the Lie derivation on NEST algebra. Mathieu[17] discribe the form of Lie derivations on primitive ring whose charater is not 2 and which has no non-trivial idempotent. After that, Miers[18],Mathieu and Villena[19] also study Lie derivations on Von Neumann algebra and algebra. Making use of the spetcial frame, I extend the discuss to the NEST algebra with the help of reference[17].