Derivable maps and derivational points

作者：Pan Zhidong^*

来源：Linear Algebra and Its Applications, 2012, 436(11): 4251-4260.

DOI：10.1016/j.laa.2012.01.027

• Derivable maps
• Derivation
• Nest

For an algebra A and an A-bimodule M, let L(A, M) be the set of all linear maps from A to M. A map delta is an element of L(A, M) is called derivable at C is an element of A if delta(A)B + A delta(B) = delta(C), for all A, B is an element of A with AB = C. We call an element C is an element of A a derivational point of L(A, M) if (sic) delta is an element of L(A, M) the condition delta is derivable at C implies delta is a derivation. We characterize derivable maps by means of Peirce decompositions and determine derivational points for some general bimodules. As a special case, we see that for a nest algebra A on a Hilbert space H. every 0 not equal C is an element of A is a derivational point of L(A, B(H)).

• 出版日期2012-6-1