76
Views
0
CrossRef citations to date
0
Altmetric
Articles

On C*-algebras of singular integral operators with PQC coefficients and shifts with fixed points

ORCID Icon, ORCID Icon & ORCID Icon
Pages 581-614 | Received 29 Dec 2020, Accepted 10 Jun 2021, Published online: 06 Jul 2021

References

  • Rabinovich V, Roch S, Silbermann B. Limit operators and their applications in operator theory. Basel: Birkhäuser; 2004.
  • Greenleaf FP. Invariant means on topological groups and their representations. New York (NY): Van Nostrand-Reinhold; 1969.
  • Gohberg I, Krupnik N. One-dimensional linear singular integral equations. Vols. I–II. Basel: Birkhäuser; 1992.
  • Duduchava RV. Integral equations with fixed singularities. Leipzig: Teubner Verlagsgesellschaft; 1979.
  • Böttcher A, Silbermann B. Analysis of Toeplitz operators. 2nd ed. Berlin: Springer; 2006.
  • Böttcher A, Karlovich YI. Carleson curves, Muckenhoupt weights, and Toeplitz operators. Basel: Birkhäuser; 1997.
  • Roch S, Santos PA, Silbermann B. Non-commutative Gelfand theories: a tool-kit for operator theorists and numerical analysts. London: Springer; 2011.
  • Sarason D. Functions of vanishing mean oscillation. Trans Amer Math Soc. 1975;207:391–405.
  • Sarason D. Toeplitz operators with piecewise quasicontinuous symbols. Indiana Univ Math J. 1977;26:817–838.
  • Power SG. Fredholm Toeplitz operators and slow oscillation. Canad J Math. 1980;32:1058–1071.
  • Beklaryan LA. Groups of homeomorphisms of the line and the circle: topological characteristics and metric invariants. Russian Math Surveys. 2004;59:599–660.
  • Karlovich YI, Kravchenko VG. An algebra of singular integral operators with piecewise-continuous coefficients and piecewise-smooth shift on a composite contour. Math USSR-Izv. 1984;23:307–352.
  • Antonevich AB. Linear functional equations: operator approach. Basel: Birkhäuser; 1996.
  • Antonevich A, Lebedev A. Functional differential equations: I. C*-theory. Harlow: Longman; 1994.
  • Kravchenko VG, Litvinchuk GS. Introduction to the theory of singular integral operators with shift. Dordrecht: Kluwer; 1994.
  • Naimark MA. Normed algebras. Groningen: Wolters-Noordhoff; 1972.
  • Douglas RG. Banach algebra techniques in operator theory. New York (NY): Academic Press; 1972.
  • Pedersen GK. C-algebras and their automorphism groups. London: Academic Press; 1979.
  • Litvinchuk GS. Boundary value problems and singular integral equations with shift (Russian). Moscow: Nauka; 1977.
  • Litvinchuk GS. Solvability theory of boundary value problems and singular integral equations with shift. Dordrecht: Kluwer; 2000.
  • Karlovich YI. The Haseman boundary value problem with slowly oscillating coefficients and shifts. In: Bini DA, Ehrhard T, Karlovich AY, et al., editors. Large truncated Toeplitz matrices, Toeplitz operators, and related topics: the Albrecht Böttcher anniversary volume. Cham: Birkhäuser/Springer; 2017. p. 463–500.
  • Karlovich YI. The local-trajectory method of studying invertibility in C∗-algebras of operators with discrete groups of shifts. Soviet Math Dokl. 1988;37:407–411.
  • Karlovich YI. A local-trajectory method and isomorphism theorems for nonlocal C∗-algebras. In: Erusalimsky YM, Gohberg I, Grudsky SM, et al., editors. Modern operator theory and applications: the Igor Borisovich Simonenko anniversary volume. Basel: Birkhäuser; 2007. p. 137–166.
  • Bastos MA, Fernandes CA, Karlovich YI. Spectral measures in C∗-algebras of singular integral operators with shifts. J Funct Anal. 2007;242:86–126.
  • Karlovich YI, Silbermann B. Local method for nonlocal operators on Banach spaces. In: Böttcher A, Gohberg I, Junghanns P, editors. Toeplitz matrices and singular integral equations: the Bernd Silbermann anniversary volume. Basel: Birkhäuser, 2002. p. 235–247.
  • Lange BV, Rabinovich VS. Pseudo-differential operators on Rn and limit operators. Math USSR Sb. 1987;57:183–194.
  • Böttcher A, Karlovich YI, Rabinovich VS. The method of limit operators for one-dimensional singular integrals with slowly oscillating data. J Oper Theory. 2000;43:171–198.
  • Quertermous KS. Fixed point composition and Toeplitz-composition C∗-algebras. J Funct Anal. 2013;265:743–764.
  • Exel R. Invertibility in grupoid C∗-algebras. In: Bastos MA, Lebre A, Samko S, et al., editors. Operator theory, operator algebras and applications. Basel: Birkhäuser/Springer; 2014. p. 173–183.
  • Shvydkoy R, Latushkin Y. Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics. J Funct Anal. 2009;257:3309–3328.
  • Silbermann B. The C∗-algebra generated by Toeplitz and Hankel operators with piecewise quasicontinuous symbols. Integr Equ Oper Theory. 1987;10:730–738.
  • Böttcher A, Roch S, Silbermann B, et al. A Gohberg-Krupnik-Sarason symbol calculus for algebras of Toeplitz, Hankel, Cauchy, and Carleman operators. In: De Branges L, Gohberg I, Rovnyak J, editors. Topics in operator theory. Ernst D. Hellinger memorial volume. Basel: Birkhäuser; 1990. p. 189–234.
  • Böttcher A, Karlovich YI, Silbermann B. Singular integral equations with PQC coefficients and freely transformed argument. Math Nachr. 1994;166:113–133.
  • Karlovich YI, Silbermann B. Fredholmness of singular integral operators with discrete subexponential groups of shifts on Lebesgue spaces. Math Nachr. 2004;272:55–94.
  • Bastos MA, Fernandes CA, Karlovich YI. C∗-algebras of singular integral operators with shifts having the same nonempty set of fixed points. Compl Anal Oper Theory. 2008;2:241–272.
  • Bastos MA, Fernandes CA, Karlovich YI. C∗-algebras of singular integral operators with shifts admitting distint fixed points. J Math Anal Appl. 2014;413:502–524.
  • Bastos MA, Fernandes CA, Karlovich YI. A C∗-algebra of singular integral operators with shifts and piecewise quasicontinuous coefficients. In: André C, Bastos MA, Karlovich AY, et al., editors. Operator theory, operator algebras and matrix theory. Basel: Birkhäuser/Springer, 2018. p. 25–64.
  • Bastos MA, Fernandes CA, Karlovich YI. Invertibility criteria in C∗-algebras of functional operators with shifts and PQC coefficients. Integr Equ Oper Theory. 2019;91:19.
  • Muhly PS, Xia J. Calderón-Zygmund operators, local mean oscillation and certain automorphisms of the Toeplitz algebra. Amer J Math. 1995;117:1157–1201.
  • Karlovich YI, Ramírez de Arellano E. Singular integral operators with fixed singularities on weighted Lebesgue spaces. Integr Equ Oper Theory. 2004;48:331–363.
  • Hagen R, Roch S, Silbermann B. Spectral theory of approximation methods for convolution equations. Basel: Birkhäuser; 1995.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.