The best approximation of classes, defined by powers of self-adjoint operators acting in Hilbert space, by other classes

V.F. Babenko (Oles Honchar Dnipropetrovsk National University),
R.O. Bilichenko (Oles Honchar Dnipropetrovsk National University)


The best approximation of class of elements such that $$$\| A^k x \| \leqslant 1$$$ by classes of elements such that $$$\| A^r x \| \leqslant N$$$, $$$N > 0$$$ for powers $$$k < r$$$ of self-adjoint operator $$$A$$$ in Hilbert space $$$H$$$ is found.


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