An extension and refinement of the theorems of Douglas and Sebestyén for unbounded operators
Year: 2026
Type: article
Abstract: For a closed densely defined operator T T from a Hilbert space H {\mathfrak {H}} to a Hilbert space K \mathfrak {K} , necessary and sufficient conditions are established for the factorization of T T with a bounded nonnegative operator X X on K \mathfrak {K} . This result yields a new extension and a refinement of a well-known theorem of R.G. Douglas [Proc. Amer. Math. Soc. 17 (1966), pp. 413–415], which shows that the operator inequality A ∗ A ≤ λ 2 B ∗ B , λ ≥ 0 A^*A\leq \lambda ^2 B^*B, \lambda \geq 0 , is equivalent to the factorization A = C B A=CB with ‖ C ‖ ≤ λ \|C\|\leq \lambda . The main results give necessary and sufficient conditions for the existence of an intermediate selfadjoint operator H ≥ 0 H\geq 0 , such that A ∗ A ≤ λ H ≤
DOI: 10.1090/proc/17514
Authors: Yosra Barkaoui, Seppo Hassi
Institution: University of Vaasa
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7124148143