巴拿赫空间中线性算子的w加权drazin广义逆的新表示.pdf

The new presentation of W-weighted Drazin generalized Inverse of Linear Operators in Banach Space Baohua Li∗ Zhiping Xiong School of Mathematics and statistics, Lanzhou University, Lanzhou 730000, P.R.China Abstract In this paper, we investigate the W-weighted Drazin generalized inverse of linear operator in Banach spaces. In our new presentation theorem, the parameter l can take any non-negative integer, therefore extending the results given in literature. Specially, as the new representation in Hilbert spaces as be concerned, we establish the iterative procedure and give the iterative error bound. Keywords: W-weighted Drazin inverse; linear operator; Banach space; Hilbert space; error bound. Mathematics Subject Classification(2000): 65F10, 65F50 1 Introduction Drazin introduced a generalized inverse of an element in a semigroups [5], and this inverse is generalized to the case of rectangular matrix by Cline-Greville [2]. Motivated by the fact that analysing Markov chains, investigating integral equations, discussing differential equations and it- erative procedures , Drazin inverse has been applied to abstract spaces. Many scholars have done much excellent work in this field recently, see [3, 10, 11, 12, 13, 14, 15, 17]. This note studies the W-weighted Drazin inverse for bounded linear operator between Banach spaces. We present a new representation with variable exponent, which extends the result in [10]. Different W-weighted Drazin inverse is obtained as the exponent varied. To begin with, let us review some notions and symbols, which may be use in the sequel. Let X and Y be Banach space (or Hilbert space ) defined over the same filed and equipped with