Moore–Penrose inverses of partitioned adjointable operators on Hilbert -modules

✍ Scribed by Qingxiang Xu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 243 KB
• Volume: 430
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2009.01.003

✦ Synopsis

A 1 h 1 + A 2 h 2 for h i ∈ H i , i = 1, 2. In this paper, several formulae for the Moore-Penrose inverse A † of A are derived, and an approach to constructing the weighted Moore-Penrose inverse from the nonweighted case is provided. In particular, the main result of Udwadia and Phohomsiri [F.E. Udwadia, P. Phohomsiri, Recursive formulas for the generalized LM-inverse of a matrix, J. Optimiz. Theory App. 131 (2006) 1-16] is generalized.