# 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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