Commutativity of unbounded representations
HTML articles powered by AMS MathViewer
- by Schōichi Ōta
- Proc. Amer. Math. Soc. 117 (1993), 1051-1056
- DOI: https://doi.org/10.1090/S0002-9939-1993-1145950-2
- PDF | Request permission
Abstract:
We introduce the notion of commutativity for unbounded representations of a ${\ast }$-algebra, and we study integrable or selfadjoint extensions, with a condition of the commutativity, of a representation.References
- H. J. Borchers, Algebraic aspects of Wightman field theory in statistical mechanics and field theory lectures, Halsted Press, New York, 1972.
- H. J. Borchers and J. Yngvason, On the algebra of field operators. The weak commutant and integral decompositions of states, Comm. Math. Phys. 42 (1975), 231–252. MR 377550
- S. Gudder and W. Scruggs, Unbounded representations of $\ast$-algebras, Pacific J. Math. 70 (1977), no. 2, 369–382. MR 482269
- Atsushi Inoue, Hideki Kurose, and Sch\B{o}ichi Ōta, Extensions of unbounded representations, Math. Nachr. 155 (1992), 257–268. MR 1231268, DOI 10.1002/mana.19921550118
- Atsushi Inoue and Kunimichi Takesue, Selfadjoint representations of polynomial algebras, Trans. Amer. Math. Soc. 280 (1983), no. 1, 393–400. MR 712267, DOI 10.1090/S0002-9947-1983-0712267-5
- Palle E. T. Jørgensen, Selfadjoint extension operators commuting with an algebra, Math. Z. 169 (1979), no. 1, 41–62. MR 546992, DOI 10.1007/BF01214912
- Palle E. T. Jorgensen, Operators and representation theory, North-Holland Mathematics Studies, vol. 147, North-Holland Publishing Co., Amsterdam, 1988. Canonical models for algebras of operators arising in quantum mechanics; Notas de Matemática [Mathematical Notes], 120. MR 919948
- Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I, Pure and Applied Mathematics, vol. 100, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. Elementary theory. MR 719020
- G. Lassner, Topological algebras of operators, Rep. Mathematical Phys. 3 (1972), no. 4, 279–293. MR 322527, DOI 10.1016/0034-4877(72)90012-2
- Sch\B{o}ichi Ōta, Commutants of unbounded derivations in $C^{\ast }$-algebras, J. Reine Angew. Math. 347 (1984), 21–32. MR 733045, DOI 10.1515/crll.1984.347.21
- Robert T. Powers, Self-adjoint algebras of unbounded operators, Comm. Math. Phys. 21 (1971), 85–124. MR 283580
- Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419 K. Schmüdgen, Unbounded operator algebras and representation theory, Akademie-Verlag, Berlin, 1988.
- S. P. Slinker, On commuting self-adjoint extensions of unbounded operators, Indiana Univ. Math. J. 27 (1978), no. 4, 629–636. MR 493477, DOI 10.1512/iumj.1978.27.27041
- A. N. Vasil′ev, The theory of representations for a topological (non-Banach) algebra with involution, Teoret. Mat. Fiz. 2 (1970), no. 2, 153–168 (Russian, with English summary). MR 473846
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 1051-1056
- MSC: Primary 46K10; Secondary 47D40
- DOI: https://doi.org/10.1090/S0002-9939-1993-1145950-2
- MathSciNet review: 1145950