The paper discusses Problems 8 and 88 posed by Stanisław Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Peller [J. Operator Theory 7 (1982)]. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper of Pełczyński and Sukochev in connection with Problem 88.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-2-7,
author = {V. V. Peller},
title = {On S. Mazur's problems 8 and 88 from the Scottish Book},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {191-198},
zbl = {1127.47027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-2-7}
}
V. V. Peller. On S. Mazur's problems 8 and 88 from the Scottish Book. Studia Mathematica, Tome 178 (2007) pp. 191-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-2-7/