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ArticleOriginal scientific text

Title

On strong generation of B(ℋ) by two commutative C*-algebras

Authors 1, 2

Affiliations

  1. Mathematisches Institut, Westfälische Wilhelms-Universität, Einsteinstraße 62, 48149 Münster, Germany
  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Poznań, Poland

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].

Bibliography

  1. J. B. Conway, A Course in Functional Analysis, Springer, New York, 1985.
  2. C. Davis, Generators of the ring of bounded operators, Proc. Amer. Math. Soc. 6 (1955), 970-972.
  3. E. A. Nordgren, M. Radjabalipour, H. Radjavi and P. Rosenthal, Quadratic operators and invariant subspaces, Studia Math. 88 (1988), 263-268.
  4. G. K. Pedersen, Analysis Now, Springer, New York, 1995.
  5. H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, Berlin, 1973.
  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.
Studia Mathematica
1997/125/2
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Pages:
175-178
Main language of publication
English
Received
1996-12-02
Published
1997
Exact and natural sciences