On strong generation of B(ℋ) by two commutative C*-algebras
Studia Mathematica (1997)
- Volume: 125, Issue: 2, page 175-178
- ISSN: 0039-3223
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topBerntzen, R., and Sołtysiak, A.. "On strong generation of B(ℋ) by two commutative C*-algebras." Studia Mathematica 125.2 (1997): 175-178. <http://eudml.org/doc/216430>.
@article{Berntzen1997,
abstract = {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].},
author = {Berntzen, R., Sołtysiak, A.},
journal = {Studia Mathematica},
keywords = {strong operator topology; family of commuting unitary operators},
language = {eng},
number = {2},
pages = {175-178},
title = {On strong generation of B(ℋ) by two commutative C*-algebras},
url = {http://eudml.org/doc/216430},
volume = {125},
year = {1997},
}
TY - JOUR
AU - Berntzen, R.
AU - Sołtysiak, A.
TI - On strong generation of B(ℋ) by two commutative C*-algebras
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 2
SP - 175
EP - 178
AB - 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].
LA - eng
KW - strong operator topology; family of commuting unitary operators
UR - http://eudml.org/doc/216430
ER -
References
top- [1] J. B. Conway, A Course in Functional Analysis, Springer, New York, 1985. Zbl0558.46001
- [2] C. Davis, Generators of the ring of bounded operators, Proc. Amer. Math. Soc. 6 (1955), 970-972. Zbl0066.09801
- [3] E. A. Nordgren, M. Radjabalipour, H. Radjavi and P. Rosenthal, Quadratic operators and invariant subspaces, Studia Math. 88 (1988), 263-268. Zbl0648.47008
- [4] G. K. Pedersen, Analysis Now, Springer, New York, 1995. Zbl0668.46002
- [5] H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, Berlin, 1973. Zbl0269.47003
- [6] W. Żelazko, Generation of B(X) by two commutative subalgebras - results and open problems, in: Functional Analysis and Operator Theory, Banach Center Publ. 30, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 1994, 363-367. Zbl0813.47056
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