2015/10/05 by Vladyslav Babenko, В. Ф. Бабенко, Babenko, Vladyslav +4
Mathematics · #26D10 #41A17 #47A58 #47A63 #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #math.FA #msc:26D10 #msc:41A17 #msc:47A58 #msc:47A63
paper · pdf · doi:10.48550/arxiv.1510.01254
arxiv created 2015/10/05 · openalex publication_date 2015/10/05 · arxiv updated 2015/10/06 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following problems: (i) the problem of approximating a function of an unbounded self-adjoint operator by bounded operators, (ii) the problem of best approximation of a certain class of elements from a Hilbert space by another class, and (iii) the problem of optimal recovery of an operator on a class of elements given with an error.