Masas in the Calkin algebra without the Continuum Hypothesis

• Autorzy: Shelah S. , Steprans J.
• Języki publikacji: EN

Abstrakty

EN

Methods for constructing masas in the Calkin algebra without assuming the Continuum Hypothesis are developed.

Słowa kluczowe

EN

Calkin algebra; almost disjoint family; mass

PL

algebra Calkina; rodzina prawie rozłączna

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2011
• Tom: Vol. 17, nr 1
• Strony: 69--89
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Shelah S.

autor

Steprans J.

• Department of Mathematics, Rutgers University, Hill Center, Piscataway, New Jersey, 08854-8019, USA,

Bibliografia

• [1] C. Akemann and N. Weaver, B(H) has a pure state that is not multiplicative on any masa, Proc. Natl. Acad. Sci. USA 105 (2008), 5313-5314.
• [2] J. Anderson, A maximal abelian subalgebra of the Calkin algebra with the extension property. Math. Scand. 42 (1978), 101-110.
• [3] J. Anderson, Extensions, restrictions, and representations of states on C*-algebras. Trans. Amer. Math. Soc. 249 (1979), 303-329.
• [4] J. Anderson, Pathology in the Calkin algebra. J. Operator Theory 2 (1979), 159-167.
• [5] B. Balcar and P. Simon, Disjoint refinement, in: Handbook of Boolean Algebras, Vol. 2, pp. 333-388, North-Holland, Amsterdam, 1989.
• [6] M. G. Bell, On the combinatorial principle P(c), Fund. Math. 114 (1981), 149-157.
• [7] K. R. Davidson, C -Algebras by Example, Fields Institute Monographs 6, American Mathematical Society, Providence, RI, 1996.
• [8] I. Farah and E. Wofsey, Set Theory and Operator Algebars, Notes from Appalachian Set Theory Workshop at Carnegie Melon University, April 2008.
• [9] P. R. Halmos, A Hilbert Space Problem Book, Graduate Texts in Mathematics 19, Encyclopedia of Mathematics and Its Applications 17, Springer-Verlag, New York, 1982.
• [10] B. E. Johnson and S. K. Parrott, Operators commuting with a von Neumann algebra modulo the set of compact operators. J. Funct. Analysis 11 (1972), 39-61.