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

V.F. Babenko; R.O. Bilichenko

doi:10.15421/240904

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), https://orcid.org/0000-0001-6677-1914
R.O. Bilichenko (Oles Honchar Dnipropetrovsk National University)

Abstract

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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References

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