Some problems of approximation theory for powers of normal operators in Hilbert space

Abstract

The best approximation of unbounded operator $A^k$ in class with $\| A^r x \| \leqslant 1$ and the best approximation of class with $\|A^k x \| \leqslant 1$ by class with $\| A^r x \| \leqslant N$, $N > 0$ for powers $k < r$ of normal operator $A$ in the Hilbert space $H$ are found.