@article{Dmytryshyn_2020, title={Approximation of positive operators by analytic vectors}, volume={12}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/4441}, DOI={10.15330/cmp.12.2.412-418}, abstractNote={<p>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 ${\mathcal E}_{q,p}^{
u,\alpha}(A)$ 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.</p>}, number={2}, journal={Carpathian Mathematical Publications}, author={Dmytryshyn, M.I.}, year={2020}, month={Dec.}, pages={412–418} }