Open AccessApproximation of unbounded functional, defined by grades of normal operator, on the class of elements of Hilbert space
Author(s) -
R.O. Bilichenko
Publication year - 2016
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241601
Subject(s) - hilbert space , mathematics , class (philosophy) , bounded function , operator space , operator (biology) , space (punctuation) , pure mathematics , multiplication operator , linear operators , bounded operator , mathematical analysis , discrete mathematics , finite rank operator , computer science , banach space , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , gene , operating system
We obtain the best approximation of unbounded functional $(A^k x; f)$ on the class $\{ x\in D(A^r) \colon \| A^r x \| \leqslant 1 \}$ by linear bounded functionals for a normal operator $A$ in the Hilbert space $H$ ($k < r$, $f\in H$).