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On the complexity of the description of $*$-algebra representations by unbounded operators

Author(s): Lyudmila Turowska
Journal: Proc. Amer. Math. Soc. 130 (2002), 3051-3065.
MSC (2000): Primary 46K10, 46L05, 47L60; Secondary 16G60
Posted: March 18, 2002
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Abstract: We study the complexity of the problem to describe, up to unitary equivalence, representations of $*$-algebras by unbounded operators on a Hilbert space. A number of examples are developed in detail.

References:

[BES]
H.Bart, T.Ehrhardt and B.Silbermann, Zero sums of idempotents in Banach algebras, Integr. Equat. Oper. Th. 19 (1994), 125-134. MR 95c:46071a
[Dal]
Yu.L. Daletskii, Continual integrals related to operator evolution equations, Uspekhi Mat. Nauk XVII (1962), no.5, 3-115.
[D]
J. Dixmier, $C^*$-algebras, North-Holland Publ. Comp., Amsterdam, 1977. MR 56:16388
[DF]
P. Donovan, M. R. Freislich, The representation theory of finite graphs and associated algebras, Carleton Mathematical Lecture Notes, No. 5. Carleton University, Ottawa, Ont., 1973, 83 pp. MR 50:9701

[JSW]
P.E.T. Jorgensen, L.M. Schmitt, R.F. Werner, Positive representations of general commutation relations allowing Wick ordering, J. Funct. Anal. 134 (1995), no. 1, 33-99. MR 96h:81033

[KS]
S. A. Kruglyak and Yu. S. Samo{\u{\i}}\kern.15emlenko, On complexity of description of representation of $*$-algebras generated by idempotents, Proc. Amer. Math. Soc., 128 (2000), no. 6, 1655-1664. MR 2000j:46099
[NT]
L. P. Nizhnik and L. B. Turowska, Representations of double commutator by matrix-differential operators, Methods Funct. Anal. Topol. 3 (1997), no. 3, 75-80. MR 2001e:47043
[OS]
V. Ostrovski{\u{\i}}\kern.15em, Yu. Samo{\u{\i}}\kern.15emlenko, Introduction to the Theory Representation of Finitely Presented $*-$algebras. $1$. Representations by bounded operators. Rev. Math. Math. Phys. 11 (1999), part 1, 1-261.
[S]
V. V. Sergeichuk, Unitary and Euclidean representations of a quiver, Linear Algebra Appl. 278 (1998), no. 1-3, 37-62. MR 99g:16020
[Pat]
A. L. T. Paterson, The class of locally compact groups $G$ for which $C^*(G)$ is amenable. Harmonic Analysis, Luxembourg, 1987, Lecture Notes in Mathematics, Vol. 1359, New York, 1988. MR 90m:22019
[Ped]
G. K. Pedersen, $C^*$-algebras and their Automorphism Groups, Academic Press, London, 1979.
[ST1]
Yu. S. Samo{\u{\i}}\kern.15emlenko and L. B. Turowska, On representations of $*$-algebras by unbounded operators, Funkt. Anal. Prilozh. 31 (1997), no. 4, 80-83.
[ST2]
Yu. S. Samo{\u{\i}}\kern.15emlenko and L. B. Turowska, On bounded and unbounded idempotents whose sum is a multiple of the identity, Preprint 2001-44, Chalmers University of Technology.
[S]
K. Schmüdgen, Unbounded operator algebras and representation theory, Akademie-Verlag, Berlin, 1990.

[Wor1]
S. L. Woronowicz, Unbounded elements affiliated with ${C}^*$-algebras and non-compact quantum groups, Commun. Math. Phys. 136 (1991), 399-432. MR 92b:46117

[WN]
S. L. Woronowicz and K. Napiorkowski, Operator theory in the $C^*$-algebra framework, Rep. Math. Phys. 31 (1992), 353-371. MR 94k:46123

[Wor2]
S. L. Woronowicz, $C^*$-algebras generated by unbounded elements, Reviews in Mathematical Physics 7 (1995), no. 3, 481-521. MR 96c:46056

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Additional Information:

Lyudmila Turowska
Affiliation: Department of Mathematics, Chalmers University of Technology, 412 96 Göteborg, Sweden
Email: turowska@math.chalmers.se

DOI: 10.1090/S0002-9939-02-06525-5
PII: S 0002-9939(02)06525-5
Keywords: $*$-algebras, $*$-representations, unbounded operators, $*$-wildness.
Received by editor(s): June 12, 2000
Received by editor(s) in revised form: November 28, 2000 and May 31, 2001
Posted: March 18, 2002
Communicated by: David R. Larson
Copyright of article: Copyright 2002, American Mathematical Society

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