Isometric automorphisms of normed linear spaces are characterized by suitable concavity properties of powers of operators. Bounded selfadjoint operators in Hilbert spaces are described by parallel concavity properties of the exponential group. Unbounded infinitesimal generators of 𝓒₀-groups of Hilbert space operators having concavity properties are characterized as well.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-26,
author = {Jan Stochel},
title = {Logarithmic concavity, unitarity and selfadjointness},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {335-348},
zbl = {1097.47021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-26}
}
Jan Stochel. Logarithmic concavity, unitarity and selfadjointness. Banach Center Publications, Tome 68 (2005) pp. 335-348. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc67-0-26/