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Algebra of possibly unbounded operators
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