The algebra B(ℋ) of all bounded operators on a Hilbert space ℋ is generated in the strong operator topology by a single one-dimensional projection and a family of commuting unitary operators with cardinality not exceeding dim ℋ. This answers Problem 8 posed by W. Żelazko in [6].
@article{bwmeta1.element.bwnjournal-article-smv125i2p175bwm,
author = {R. Berntzen and A. So\l tysiak},
title = {On strong generation of B(H) by two commutative C*-algebras},
journal = {Studia Mathematica},
volume = {122},
year = {1997},
pages = {175-178},
zbl = {0891.47029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i2p175bwm}
}
Berntzen, R.; Sołtysiak, A. On strong generation of B(ℋ) by two commutative C*-algebras. Studia Mathematica, Tome 122 (1997) pp. 175-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i2p175bwm/
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