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)


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


normal operator; functional; decomposition of unity; Hilbert space


Arestov V.V. "Approximation of unbounded operators by the bounded ones and related extremum problems", Uspekhi mat. nauk, 1996; 51(6): pp. 89-124. (in Russian)

Babenko V.F., Bilichenko R.O. "Inequalities of Taikov type for self-adjoint operators in Hilbert space", Trudy IPMM, 2010; 21: pp. 11-18. (in Russian)

Babenko V.F., Bilichenko R.O. "Inequalities of Taikov type for grades of normal operators in Hilbert space", Dnipr. Univ. Math. Bull., 2011; 16: pp. 3-7. (in Russian)

Babenko V.F., Bilichenko R.O. "Approximation of unbounded functionals by the bounded ones in Hilbert space", Dnipr. Univ. Math. Bull., 2012; 17; pp. 3-10. (in Russian)

Berezanskij Yu.M., Us G.F., Sheftel' Z.G. Functional analysis, Kyiv, 1990; 600 p. (in Russian)

Babenko V.F., Korneichuk N.P., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Naukova dumka, Kyiv, 2003; 590 p. (in Russian)

Stechkin S.B. "Inequalities between norms of derivatives of arbitrary function", Acta scient. math., 1965; 26: pp. 225-230. (in Russian)

Stechkin S.B. "The best approximation of linear operators", Matem. zametki, 1967; 1(2): pp. 137-148. (in Russian)

Taikov L.V. "Inequalities of Kolmogorov type and formulas of numeric differentiation", Matem. zametki, 1968; 4(2): pp. 223-238. (in Russian)

Shadrin A.Yu. "Inequalities of Kolmogorov type and estimates of spline-interpolation for periodic classes $$$W^m_2$$$", Matem. zametki, 1990; 48(4): pp. 132-139. (in Russian)


  • There are currently no refbacks.

Copyright (c) 2016 R.O. Bilichenko

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Registered in

Not much? See «Misleading Metrics» [web-archive] (by J. Beall), «The story of fake impact factor companies ...» (by M. Jalalian); on the other hand, see «Citation Statistics» (by R. Adler, J. Ewing, P. Taylor)

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