Approximation of unbounded functional, defined by grades of normal operator, on the class of elements of Hilbert space

R.O. Bilichenko

doi:10.15421/241601

Approximation of unbounded functional, defined by grades of normal operator, on the class of elements of Hilbert space

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

Abstract

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 $$$H$$$ ($$$k < r$$$, $$$f\in H$$$).

Keywords

normal operator; functional; decomposition of unity; Hilbert space

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