Abstract
The purpose of this note is twofold. First to present a conjecture concerning the form of the pure states on B(H) and second to prove a theorem related to this conjecture.
This work is an expanded version of a talk given at the Vth Operator Theory conference held June 2–12, 1980, in Timişoara and Herculane, Romania.
Research supported in part by a grant from the National Science Foundation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alfsen, E.M.: Compact convex sets and boundary integrals, Springer-Verlag, New York/Heidelberg/Berlin, 1971.
Anderson, J.: Extensions, restrictions and representations of states on C*-algebras, Trans. Amer. Math. Soc. 249 (1979), 303–329.
Anderson, J.: Extreme points in sets of positive linear maps on B(H), J. Functional Analysis 31 (1979), 195–217.
Anderson, J.: A maximal abelian subalgebra with the extention property, Math. Scand. 42 (1978), 010–110.
Anderson, J.: Pathology in the Calkin algebra, J.Operatot Theory 2 (1979), 159–167.
Kadison, R.V.; Singer, I.M.: Extensions of pure states, Amer. J. Math. 81 (1959), 383–400.
Powers, R.T.: Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. Math. 86 (1967), 138–171.
Wils, I.M.: Stone-Čech compactifications and representations of operator algebras, Ph.D. thesis, Catholic University of Nijmegen, 1968.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer Basel AG
About this chapter
Cite this chapter
Anderson, J. (1981). A Conjecture Concerning the Pure States of B(H) and a Related Theorem. In: Apostol, C., Douglas, R.G., Nagy, B.S., Voiculescu, D., Arsene, G. (eds) Topics in Modern Operator Theory. Operator Theory: Advances and Applications, vol 2. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5456-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-5456-6_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1244-2
Online ISBN: 978-3-0348-5456-6
eBook Packages: Springer Book Archive