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

R.O. Bilichenko (Oles Honchar Dnipropetrovsk National University)


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.


normal operator; spectral theorem; Stechkin's problem


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