Approximation of unbounded operators by bounded operators in a Hilbert space

• Date: 2009
• Main Authors: Bilichenko, R. O., Babenko, V. F., Биличенко, Р. О., Бабенко, В. Ф.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3010
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We determine the best approximation of an arbitrary power $A^k$ of an unbounded self-adjoint operator $A$ in a Hilbert space $H$ on the class $\{x ∈ D(A^r ) : ∥A^r x∥ ≤ 1\},\; k < r$.