ncku-talk2012-09-27

NCTS(South)/ NCKU Math Colloquium

DATE 2012-09-27　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Prof. Peng Cao（Department of Mathematics, Beijing Institute of Technology）

TITLE Banach Algebras Generated by Lie Subalgebras

ABSTRACT For every Banach algebra A, it can be seen as a Lie algebra, since the commutator operation can be seen as the Lie product: [x,y] = xy - yx. Let L be a Lie subalgebra of A: The Banach algebra generated by L, denoted by A(L), is the smallest Banach algebra containing L in A. In this talk, we will consisder the properties of A(L) if L has some "good" conditions. Firstly, we will generalise the definition of nilpotent Lie algebras to Engel Lie algebras. Then under some additional conditions, we will give some conditions of L which are equivalent with A(L) is commutative modulo the Jacobson Radical. We show that A(L) has much stronger properties if L is Engel. Finally, we will apply these results to polynomial compact operators.

NCTS(South)/ NCKU Math Colloquium

DATE	2012-09-27　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Prof. Peng Cao（Department of Mathematics, Beijing Institute of Technology）

TITLE	Banach Algebras Generated by Lie Subalgebras

ABSTRACT	For every Banach algebra A, it can be seen as a Lie algebra, since the commutator operation can be seen as the Lie product: [x,y] = xy - yx. Let L be a Lie subalgebra of A: The Banach algebra generated by L, denoted by A(L), is the smallest Banach algebra containing L in A. In this talk, we will consisder the properties of A(L) if L has some "good" conditions. Firstly, we will generalise the definition of nilpotent Lie algebras to Engel Lie algebras. Then under some additional conditions, we will give some conditions of L which are equivalent with A(L) is commutative modulo the Jacobson Radical. We show that A(L) has much stronger properties if L is Engel. Finally, we will apply these results to polynomial compact operators.