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

• Autorzy: R. Berntzen , A. Sołtysiak
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 47C15: Operators in C * - or von Neumann algebras
• 47A15: Invariant subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 125
• Numer: 2
• Strony: 175-178

Daty

wydano

1997

otrzymano

1996-12-02

Twórcy

autor

R. Berntzen

• Mathematisches Institut, Westfälische Wilhelms-Universität, Einsteinstraße 62, 48149 Münster, Germany

autor

A. Sołtysiak

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Poznań, Poland

Bibliografia

• [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.