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

References


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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557