Generation of B(X) two commutative subalgebras - results and open problems

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1. [1] B. Aniszczyk, R. Frankiewicz and C. Ryll-Nardzewski, An example of a nonseparable Banach algebra without nonseparable commutative subalgebras, Studia Math. 93 (1989), 287-289. Zbl0699.46028
2. [2] C. Davis, Generators of the ring of bounded operators, Proc. Amer. Math. Soc. 6 (1955), 970-972. Zbl0066.09801
3. [3] R. G. Douglas and C. Pearcy, von Neumann algebras with a single generator, Michigan Math. J. 16 (1969), 21-26. Zbl0175.44301
4. [4] R. C. James, A nonreflexive Banach space isometric with its second conjugate, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 174-177. Zbl0042.36102
5. [5] B. S. Mityagin and I. Ts. Èdelshteĭn, Homotopy type of linear groups for two classical Banach spaces, Funktsional. Anal. i Prilozhen. 4 (3) (1970), 61-72 (in Russian). 
6. [6] V. Müller and W. Żelazko, B(X) is generated in strong topology by two of its elements, Czechoslovak Math. J. 39 (114) (1989), 486-489. Zbl0717.47017
7. [7] E. A. Nordgren, M. Radjabalipour, H. Radjavi and P. Rosenthal, Quadratic operators and invariant subspaces, Studia Math. 88 (1988), 263-268. Zbl0648.47008
8. [8] C. L. Olsen and W. R. Zame, Some C*-algebras with single generator, Trans. Amer. Math. Soc. 215 (1976), 205-217. Zbl0342.46047
9. [9] C. Pearcy, W*-algebras with a single generator, Proc. Amer. Math. Soc. 13 (1962), 831-832. Zbl0127.33002
10. [10] C. Pearcy, On certain von Neumann algebras which are generated by partial isometries, ibid. 15 (1964), 393-395. Zbl0135.16803
11. [11] T. Saitô, On generators of von Neumann algebras, Michigan Math. J. 15 (1968), 373-376. Zbl0175.14103
12. [12] P. Šemrl, On algebraic generation of B(X) by two subalgebras with square zero, Studia Math. 97 (1991), 139-142. Zbl0747.47027
13. [13] N. Suzuki and T. Saitô, On the operators which generate continuous von Neumann algebras, Tôhoku Math. J. (2) 15 (1963), 277-280. Zbl0194.15903
14. [14] D. M. Topping, UHF algebras are singly generated, Math. Scand. 22 (1968), 224-226 (1969). Zbl0172.41303
15. [15] A. Wilansky, Subalgebras of B(X), Proc. Amer. Math. Soc. 22 (1971), 355-360. 
16. [16] W. Wogen, On generators for von Neumann algebras, Bull. Amer. Math. Soc. 75 (1969), 95-99. Zbl0185.21203
17. [17] W. Żelazko, B(H) is generated by two of its abelian subalgebras, in: Invariant Subspaces and Allied Topics, Narosa Publ. House, 1990, 144-146. 
18. [18] W. Żelazko, Algebraic generation of B(X) by two subalgebras of square zero, Studia Math. 90 (1988), 205-212. 
19. [19] W. Żelazko, B(X) is generated in strong operator topology by two subalgebras with square zero, Proc. Roy. Irish Acad. Sect. A 88 (1988), 19-21. Zbl0675.47044
20. [20] W. Żelazko, Concerning generation of B(X) by two subalgebras with square zero, Funct. Approx. Comment. Math., to appear. Zbl0804.46055

1. R. Berntzen, A. Sołtysiak, On strong generation of B(ℋ) by two commutative C*-algebras