Approximation of positive operators by analytic vectors

Array

Authors

  • M.I. Dmytryshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-3248-7736

DOI:

https://doi.org/10.15330/cmp.12.2.412-418

Keywords:

positive operator, approximation space, Bernstein-Jackson-type inequality

Abstract

We give the estimates of approximation errors while approximating of a positive operator $A$ in a Banach space by analytic vectors. Our main results are formulated in the form of Bernstein and Jackson type inequalities with explicitly calculated constants. We consider the classes of invariant subspaces ${\mathcal E}_{q,p}^{\nu,\alpha}(A)$ of analytic vectors of $A$ and the special scale of approximation spaces $\mathcal {B}_{q,p,\tau}^{s,\alpha}(A)$ associated with the complex degrees of positive operator. The approximation spaces are determined by $E$-functional, that plays a similar role as the module of smoothness. We show that the approximation spaces can be considered as interpolation spaces generated by $K$-method of real interpolation. The constants in the Bernstein and Jackson type inequalities are expressed using the normalization factor.

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Published

2020-12-27

How to Cite

(1)
Dmytryshyn, M. Approximation of Positive Operators by Analytic Vectors: Array. Carpathian Math. Publ. 2020, 12, 412-418.

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Section

Scientific articles