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)^[1] and (Uhlmann 1962), who studied some examples of O*-algebras, called Borchers algebras, arising from the Wightman axioms of quantum field theory. Powers (1971)^[2] and (Lassner 1972) began the systematic study of algebras of unbounded operators.

References

↑ Borchers, H. -J. (April 1962). "On structure of the algebra of field operators" (in en). Il Nuovo Cimento 24 (2): 214–236. doi:10.1007/BF02745645. ISSN 0029-6341. http://link.springer.com/10.1007/BF02745645.
↑ Powers, Robert T. (June 1971). "Self-adjoint algebras of unbounded operators" (in en). Communications in Mathematical Physics 21 (2): 85–124. doi:10.1007/BF01646746. ISSN 0010-3616. http://link.springer.com/10.1007/BF01646746.

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, doi:10.1007/bf01608975, ISSN 0010-3616, Bibcode: 1975CMaPh..42..231B, 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, Bibcode: 1972RpMP....3..279L
Schmüdgen, Konrad (1990), Unbounded operator algebras and representation theory, Operator Theory: Advances and Applications, 37, Birkhäuser Verlag, doi:10.1007/978-3-0348-7469-4, ISBN 978-3-7643-2321-9
Uhlmann, Armin (1962), "Über die Definition der Quantenfelder nach Wightman und Haag", Wiss. Z. Karl-Marx-Univ. Leipzig Math.-Nat. Reihe 11: 213–217

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/O*-algebra. Read more

[1] Borchers, H. -J. (April 1962). "On structure of the algebra of field operators" (in en). Il Nuovo Cimento 24 (2): 214–236. doi:10.1007/BF02745645. ISSN 0029-6341. http://link.springer.com/10.1007/BF02745645.

[2] Powers, Robert T. (June 1971). "Self-adjoint algebras of unbounded operators" (in en). Communications in Mathematical Physics 21 (2): 85–124. doi:10.1007/BF01646746. ISSN 0010-3616. http://link.springer.com/10.1007/BF01646746.

[1]

[2]