O*-algebra

In mathematics, an O*-algebra is an algebra of possibly unbounded operators defined on a dense subspace of a Hilbert space. The original examples were described by Borchers (1962) and Uhlmann (1962), who studied some examples of O*-algebras, called Borchers algebras, arising from the Wightman axioms of quantum field theory. Powers (1971) and Lassner (1972) began the systematic study of algebras of unbounded operators.

References

• Borchers, H.-J. (1962), "On structure of the algebra of field operators", Nuovo Cimento (10) 24: 214–236, doi:10.1007/BF02745645, MR0142320 
• Borchers, H. J.; Yngvason, J. (1975), "On the algebra of field operators. The weak commutant and integral decompositions of states", Communications in Mathematical Physics 42: 231–252, ISSN 0010-3616, MR0377550, http://projecteuclid.org/euclid.cmp/1103899047 
• Lassner, G. (1972), "Topological algebras of operators", Reports on Mathematical Physics 3 (4): 279–293, doi:10.1016/0034-4877(72)90012-2, ISSN 0034-4877, MR0322527 
• Powers, Robert T. (1971), "Self-adjoint algebras of unbounded operators", Communications in Mathematical Physics 21: 85–124, ISSN 0010-3616, MR0283580, http://projecteuclid.org/euclid.cmp/1103857289 
• Schmüdgen, Konrad (1990), Unbounded operator algebras and representation theory, Operator Theory: Advances and Applications, 37, Birkhäuser Verlag, ISBN 978-3-7643-2321-9, MR1056697 
• Uhlmann, Armin (1962), "Über die Definition der Quantenfelder nach Wightman und Haag", Wiss. Z. Karl-Marx-Univ. Leipzig Math.-Nat. Reihe 11: 213–217, MR0141413