2025/07/17 by Yosra Barkaoui, Barkaoui, Yosra, Seppo Hassi +1 · 1 citation
Mathematics · #47A07 #47A62 #47A63 #47B02 #47B25 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2507.13561
openalex publication_date 2025/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a closed densely defined operator T from a Hilbert space \mathfrakH to a Hilbert space \mathfrakK, necessary and sufficient conditions are established for the factorization of T with a bounded nonnegative operator X on \mathfrakK. This result yields a new extension and a refinement of a well-known theorem of R.G. Douglas, which shows that the operator inequality A^*A≤ λ2 B^*B, λ≥ 0, is equivalent to the factorization A=CB with ‖C‖≤ λ. The main results give necessary and sufficient conditions for the existence of an intermediate selfadjoint operator H≥ 0, such that A^*A ≤ λH ≤ λ2 B^*B. The key results are proved by first extending a theorem of Z. Sebestyén to the setting of unbounded operators.