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, 24 (2): 214–236, Bibcode:1962NCim...24..214B, doi:10.1007/BF02745645, MR 0142320
• 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 (3): 231–252, Bibcode:1975CMaPh..42..231B, doi:10.1007/bf01608975, ISSN 0010-3616, MR 0377550
• Lassner, G. (1972), "Topological algebras of operators", Reports on Mathematical Physics, 3 (4): 279–293, Bibcode:1972RpMP....3..279L, doi:10.1016/0034-4877(72)90012-2, ISSN 0034-4877, MR 0322527
• Powers, Robert T. (1971), "Self-adjoint algebras of unbounded operators", Communications in Mathematical Physics, 21 (2): 85–124, Bibcode:1971CMaPh..21...85P, doi:10.1007/bf01646746, ISSN 0010-3616, MR 0283580
• Schmüdgen, Konrad (1990), Unbounded operator algebras and representation theory, Operator Theory: Advances and Applications, vol. 37, Birkhäuser Verlag, doi:10.1007/978-3-0348-7469-4, ISBN 978-3-7643-2321-9, MR 1056697
• Uhlmann, Armin (1962), "Über die Definition der Quantenfelder nach Wightman und Haag", Wiss. Z. Karl-Marx-Univ. Leipzig Math.-Nat. Reihe, 11: 213–217, MR 0141413