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
Further reading 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 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