Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 20 (2025), 193 -- 201

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This work is licensed under a Creative Commons Attribution 4.0 International License.

SOME METRIC CHARACTERIZATIONS OF COMMUTATIVITY IN C*-ALGEBRAS

Florin Pop

Abstract. We study Le Page's theorem in the context of C*-algebras and obtain several characterizations of commutativity and centrality implied by identities or inequalities satisfied by the norm.

2020 Mathematics Subject Classification: 46L05, 46L10, 47A30
Keywords: von Neumann algebra, C*-algebra, norm, commutativity, center

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References

  1. B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math., vol. 735, Springer-Verlag, 1979. Zbl 0409.46054.

  2. W. B. Arveson, Notes on extensions of C*-algebras, Duke Math. J., 44 (1977), 329--355. MR0438137. Zbl 0368.46052.

  3. J. W. Baker and J. S. Pym, A remark on continuous bilinear mappings, Proc. Edinburgh Math. Soc., 17 (1970/71), 245--248. MR0303291. Zbl 0217.44801.

  4. M. J. Crabb, J. Duncan, and C. M. McGregor, Characterizations of commutativity for C*-algebras, Glasgow Math. J., 15 (1974), 172--175. MR0361807. Zbl 0301.46047.

  5. K. R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series 191, 1988. Zbl 0669.47024.

  6. K. R. Davidson, C*-algebras by example, Fields Institute Monographs, American Mathematical Society, 1996. Zbl 0958.46029.

  7. J. Erdos, The triangular factorization of operators on Hilbert space, Indiana Univ. Math. J. , 22 (1973), 939--950. MR0336404. Zbl 0245.47020.

  8. J. Glimm and R. V. Kadison, Unitary operators in C*-algebras, Pacific J. Math., 10 (1960), 547--556. MR0115104. Zbl 0152.33001.

  9. C. Le Page, Sur quelques conditions entraînant la commutativité dans les algèbres de Banach, C. R. Acad. Sci. Paris Ser A-B 265 (1967), 235-237. MR0226409. Zbl 0158.14102 .

  10. M. Oudadess, Commutativity conditions in algebras with C*-equalities, Comm. Math. Appl. 3 (2012), 61--73.

  11. M. Oudadess and Y. Tsertos, Commutativity results in non unital real topological algebras, Appl. Appl. Math., 7 (2012), 164--174. MR2945907.

  12. V. I. Paulsen, Completely Bounded Maps and Operator Algebras, Cambridge University Press, 2003. MR1976867. Zbl 1029.47003.

  13. S. C. Power, Factorization in analytic operator algebras, J. Funct. Anal., 67 (1986), 413--432. MR0845465. Zbl 0591.47017.



Florin Pop
Department of Mathematics, Wagner College,
Staten Island, NY 10314, U.S.A.
e-mail: fpop@wagner.edu

https://www.utgjiu.ro/math/sma