Hostname: page-component-cb9f654ff-5jtmz Total loading time: 0 Render date: 2025-09-01T06:22:18.924Z Has data issue: false hasContentIssue false
  • English
  • Français

Characters on C*-algebras, the joint normal spectrum, and a pseudo-differential C*-algebra

Published online by Cambridge University Press:  20 January 2009

S. C. Power
S. C. Power
Affiliation:
Department of MathematicsUniversity of Lancaster
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let {Ai; i ∈ Ω} be a family of C*-algebras acting on a Hubert space H and let A be the C*-algebra that they generate. We shall assume throughout that C*-algebras always contain the identity operator. Let M(A) denote the space of characters, that is, multiplicative linear functionals, acting on A, with the weak star topology. We obtain here a natural characterisation of M(A) as a subset of the product space determined by {M(Ai); i ∈ Ω}. In the case of singly generated C*-algebras this characterisation is related to the joint normal spectrum (5) of a family of operators.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 1 , February 1981 , pp. 47 - 53
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Bunce, J., The joint spectrum of commuting non normal operators, Proc. Amer. Math. Soc. 29 (1971), 499–505.CrossRefGoogle Scholar
(2)Cordes, H. O., On compactness of commutators of multiplications and convolutions, and boundedness of pseudo-differential operators, J. Functional Analysis 18 (1975), 115–131.CrossRefGoogle Scholar
(3)Douglas, R. G., Banach algebra techniques in operator theory (Academic Press, New York, 1972).Google Scholar
(4)Herman, E., The symbol of the algebra of singular integral operators, J. Math. Mech 15 (1966), 147–155.Google Scholar
(5)Lee, S. G., (Thesis, Univ. of California at Santa Barbara, 1972).Google Scholar
(6)Moyer, R. D., Computation of symbols on C*-algebras of singular integral operators, Bull. Amer. Math. Soc. 77 (1971), 615–620.CrossRefGoogle Scholar
(7)Power, S. C., Commutator ideals and pseudo-differential C*-algebras, Quart. J. Math. Oxford (2) 31 (1980), 467–489.CrossRefGoogle Scholar
(8)Taylor, M. E., Gelfand theory of pseudo-differential operators and hypoelliptic operators, Trans. Amer. Math. Soc. 153 (1971), 495–510.CrossRefGoogle Scholar
(9)Taylor, M. E., Pseudo -differential operators, (Springer Verlag lecture notes, no. 416).Google Scholar