Open AccessApproximation of unbounded functionals by the bounded ones in Hilbert space
Author(s) -
В. Ф. Бабенко,
R.O. Bilichenko
Publication year - 2012
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241201
Subject(s) - bounded function , hilbert space , mathematics , bounded operator , space (punctuation) , class (philosophy) , operator (biology) , mathematical analysis , operator space , pure mathematics , linear operators , finite rank operator , banach space , computer science , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , gene , operating system
We obtained the value of the best approximation of unbounded functional $F_f(x) = (A^kx, f)$ on the class $\{ x\in D(A^r) \colon \| A^r x \| \leqslant 1 \}$ by linear bounded functionals ($A$ is a self-adjoint operator in the Hilbert space $H$, $f\in H$, $k < r$).