Abstract
In this paper, by using the notion of convolution types we introduce symmetric and non-symmetric convolution type \(\hbox {C}^*\)-algebras. It is shown that any (exact) convolution type induces a (an exact) functor on the category of \(\hbox {C}^*\)-algebras. In particular, any group induces a convolution type and a functor on the category of \(\hbox {C}^*\)-algebras. It is also shown that discrete crossed product of \(\hbox {C}^*\)-algebras and discrete inverse semigroup \(\hbox {C}^*\)-algebras can be considered as convolution type \(\hbox {C}^*\)-algebras.
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References
Araùjo, J., Bünau, P.V., Mitchell, J.D., Neunhöffer, M.: Computing automorphisms of semigroups. J. Symb. Comput. 45(3), 373–392 (2010)
Brunotte, H.: Discrete convolution rings. Rom. J. Math. Comput. Sci. 3(2), 155–159 (2013)
Carando, D., Sevilla-Peris, P.: On the convergence of some classes of Dirichlet series. Proceedings of the XIIth “Dr. Antonio A. R. Monteiro” Congress, 57–66, Actas Congr. “Dr. Antonio A. R. Monteiro”, Univ. Nac. del Sur, Bahía Blanca (2014)
D’Ambrosio, L.: Extension of Bernstein polynomials to infinite dimensional case. J. Approx. Theory 140(2), 191–202 (2006)
Davidson, K.: \(\text{ C }^*\)-algebras by Example. Fields Institute Monographs, vol. 6. American Mathematical Society, Providence (1996)
East, J., Nordahi, T.: On groups generated by involutions of a semigroup. J. Algebra 445, 136–162 (2016)
El Bachraoui, M.: Convolution over Lie and Jordan algebras. Contrib. Discrete Math. 1(1), 106–126 (2006)
Khoshkam, M., Skandalis, G.: Crossed products of \(C^*\)-algebras by groupoids and inverse semigroups. J. Oper. Theory 51(2), 255–279 (2004)
Murphy, G.J.: \(\text{ C }^\ast \)-algebras and operator theory. Academic Press Inc, Boston (1990)
Nourouzi, K., Reza, A.: Functors induced by Cauchy extensions of \(\text{ C }^\ast \)-algebras. Sahand Commun. Math Anal. 14(1), 27–53 (2019)
Pedersen, G.K.: \(\text{ C }^\ast \)-algebras and their Automorphism Groups, London Mathematical Society Monographs, vol. 14. Academic Press Inc [Harcourt Brace Jovanovich, Publishers], London (1979)
Queffélec, H.: H. Bohr’s vision of ordinary Dirichlet series; old and new results. J. Anal. 3, 43–60 (1995)
Rotman, J.J.: An introduction to homological algebra. Universitext, 2nd edn. Springer, New York (2009)
Rudin, W.: Functional Analysis. International Series in Pure and Applied Mathematics, 2nd edn. McGraw-Hill Inc, New York (1991)
Veldsman, S.: Convolution rings. Algebra Colloq. 13(2), 211–238 (2006)
Veldsman, S.: Arithmetic convolution rings. Int. J. Algebra 5(13–16), 771–791 (2011)
Williams, D.P.: Crossed Products of \(\text{ C }^\ast \)-algebras. Mathematical Surveys and Monographs, vol. 134. American Mathematical Society, Providence (2007)
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The authors would like to thank the anonymous referee for his/her constructive and valuable comments which helped improve the quality of the paper.
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Communicated by Hamid Reza Ebrahimi Vishki.
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Nourouzi, K., Reza, A. Convolution Type \(\hbox {C}^*\)-Algebras . Bull. Iran. Math. Soc. 46, 777–798 (2020). https://doi.org/10.1007/s41980-019-00292-6
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DOI: https://doi.org/10.1007/s41980-019-00292-6