2017/04/25 by S. H. Kulkarni, Kulkarni, S. H., G. Ramesh +1
Mathematics · #47A05 #47A10 #47A50 #47A55 #47A58 #47A75 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1704.07534
openalex publication_date 2017/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H1, H2 be complex Hilbert spaces and T be a densely defined closed linear operator from its domain D(T), a dense subspace of H1, into H2. Let N(T) denote the null space of T and R(T) denote the range of T. Recall that C(T) := D(T) ∩ N(T)⊥ is called the \it carrier space of T and the \it reduced minimum modulus γ(T) of T is defined as: γ(T) := inf \‖T(x)‖ : x ∈ C(T), ‖x‖ = 1 \ . Further, we say that T \it attains its reduced minimum modulus if there exists x0 ∈ C(T) such that ‖x0‖ = 1 and ‖T(x0)‖ = γ(T). We discuss some properties of operators that attain reduced minimum modulus. In particular, the following results are proved.