2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126382The paper discusses Problems 8 and 88 posed by Stanislaw Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Section 5 of my paper "Estimates of functions of power bounded operators on Hilbert spaces", J. Operator Theory 7 (1982), 341-372. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper by Pelczynski and Sukochev.8 pagesFunctional AnalysisClassical Analysis and ODEsComplex Variables46B28; 47B35; 46E35text