Multiplicative Lower-Upper Triangular Decompositions of Operators
Israel Gohberg, M. A. Kaashoek, Seymour Goldberg · Birkhäuser Basel eBooks · 1993
In Chapter XX we dealt with the problem of additive LU- decompositions of operators with respect to a chain. In this chapter we are concerned with the more challenging problem of multiplicative LU -decomposition of certain operators. The theorems which are presented encompass classical results from Linear Algebra which show that, under certain conditions, a matrix can be represented as a product of a lower with an upper triangular matrix. Also, the possibility of factoring certain integral operators as the product of integral operators with lower and upper triangular kernel functions is treated as a special case of the general theory which we now develop. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.