Perturbation of closed range operators and Moore-Penrose inverse

2015/10/06 by S. H. Kulkarni, Kulkarni, S. H., G. Ramesh +1
Computer Science · Mathematics · #47A55 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.FA #msc:47A55

paper · pdf · doi:10.48550/arxiv.1510.01534

openalex publication_date 2015/10/06 · arxiv created 2015/10/07 · arxiv updated 2015/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H₁,H₂ be complex Hilbert spaces and T:H₁→ H₂ be a densely defined closed operator with domain D(T)⊆ H₁ and T^† be the Moore-Penrose inverse of T. Let S:H₁→ H₂ be a bounded operator. In this article we focus our attention on the following questions: 1. Under what conditions closedness of range of T will imply the closedness of range of T+S? 2. What is the relation between T^† and (T+S)^†? 3. What is the relation between T^† and S^†?.

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