Auxiliary material

  • Albrecht Böttcher
  • Bernd Silbermann
Part of the Springer Monographs in Mathematics book series (SMM)


Let X and Y be Banach spaces. We denote by. ℒ(X, Y) the linear space of all (bounded and linear) operators from X to Y. We (X, Y) ⊂ (X, Y) denote the collection of all compact operators from X into Y, and 0(X, Y) refers to the set of all finite-rank operators from X into Y, i.e., F is in 0(X, Y) if and only if F(X, Y) and dim F(X) < ∞. In the case X = Y we shall write (X) = ℒ(X, X), (X) = (X, X), 0(X) = ℓ 0(X, X).


Banach Space Maximal Ideal Banach Algebra Singular Integral Operator Fredholm Operator 
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Notes and comments

  1. [2]
    Clancey, K., and I. Gohberg Factorization of matrix functions and singular integral operators. Birkhäuser Verlag, Basel 1981.Google Scholar
  2. [1]
    Reed, M., and B. Simon Methods of modern mathematical physics. Vol. I—IV. Academic Press, New York 1972–1979; Russian transi.: Mir, Moscow 1977–1982.Google Scholar
  3. [1]
    Verbitski, I. E., and N. YA. Krupnik On the applicability of the reduction method to discrete Wiener-Hopf equations with piecewise continuous symbol. In: Spektr. Svoistva Oper. (Mat. Issled., Vyp. 45), 17–28, Shtiintsa, Kishinev 1977 ( Russian).Google Scholar
  4. [1]
    Böttcher, A., N. Krupnik, and B Silbermann A general look at local principles with special emphasis on the norm computation aspect. Integral Equations and Operator Theory 11: 4, 455–479 (1988).MathSciNetMATHCrossRefGoogle Scholar
  5. [1]
    Burckel, R. B. Bishop’s Stone-Weierstraß theorem. Amer. Math. Monthly 91: 1, 22–32 (1984).MathSciNetMATHCrossRefGoogle Scholar
  6. [1]
    Machado, S. On Bishop’s generalization of the WeierstraB-Stone theorem. Indagationes Math. 39, 218–224 (1977).MathSciNetCrossRefGoogle Scholar
  7. [1]
    Szymanski, W. Antisymmetry of subalgebras of C*-algebras. Stud. Math. 60: 1, 97–107 (1977).Google Scholar
  8. [1]
    Ransford, T. J. A short elementary proof of the Bishop-Stone-Weierstraß theorem. Math. Proc. Camb. Phil. Soc. 96, 309–311 (1984).Google Scholar
  9. [1]
    Glicksberg, I. Measures orthogonal to algebras and sets of antisymmetry. Trans. Amer. Math. Soc. 105, 415–435 (1962).MathSciNetMATHCrossRefGoogle Scholar
  10. [1]
    Gelfand, I. M., D. A. Raikov, and G. E. Shilov Kommutative normierte Algebren. VEB Deutscher Verlag der Wissenschaften, Berlin 1964; Russian original: Fizmatgiz, Moscow 1960.Google Scholar
  11. [1]
    Gebonimus, YA. L. On a problem of G. Szegö, M. Kac, G. Baxter, and I. Hirschman. Izv. Akad. Nauk SSSR, Ser. Mat., 31, 289–304 (1967) (Russian).Google Scholar
  12. [1]
    Coburn, L. A., and R. G. Douglas Translation operators on a half-line. Proc. Nat. Acad. Sci. USA 62, 1010–1013 (1969).MathSciNetMATHCrossRefGoogle Scholar
  13. [1]
    Zelazko, W. On a certain class of non-removable ideals in Banach algebras. Studia Math. 44, 87–92 (1972).MathSciNetMATHGoogle Scholar
  14. [1]
    Devinatz, A., and M. Shinbrot General Wiener-Hopf operators. Trans. Amer. Math. Soc. 145, 467–494 (1969). DIXMIER, JGoogle Scholar
  15. [2]
    Kozak, A. V. A local principle in the theory of projection methods. Dokl. Akad. Nauk SSSR 212: 6, 1287 to 1289 (1973) Russian); also in: Soviet Math. Dokl. 14, 1580–1583 (1974).Google Scholar
  16. [3]
    Kozak, A. V. Projection methods for the solution of multidimensional equations of convolution type. Cand. Dissert., Rostov-on-Don State Univ. 1974 ( Russian).Google Scholar
  17. [4]
    Kozak, A. V. A local principle in the theory of projection methods. In: Differ. Integr. Uravn. Prilozh., 58–72, Izd. Kalmyk. and Rostov. Univ., Elista 1983 ( Russian).Google Scholar
  18. [1]
    Mikhlin, S. G. Singular integral equations. Uspehi Mat. Nauk. 3: 3, 29–112 (1948) (Russian).Google Scholar
  19. [1]
    Prössdorf, S., and B Silbermann Projektionsverfahren und die näherungsweise Lösung singulärer Gleichungen. Teubner-Texte zur Mathematik, Teubner, Leipzig 1977.Google Scholar
  20. [1]
    Clancey, K. F., and J. A. Gosselin On the local theory of Toeplitz operators. Illinois J. Math. 22: 3, 449–458 (1978).MathSciNetMATHGoogle Scholar
  21. [1]
    Clancey, K. F., and B. B. Morrel The essential spectrum of some Toeplitz operators. Proc. Amer. Math. Soc. 44: 1, 129 —134 (1974).Google Scholar
  22. [2]
    Gohberg, I., and N. YA. Krupnik On the algebra generated by one-dimensional singular integral operators with piecewise continuous coefficients. Funkts. Anal. Prilozh. 4: 3, 26–36 (1970)Russian); also in: Funct. Anal. Appl. 4, 193–201 (1970).Google Scholar
  23. [1]
    Duren, P. L. Theory of HP spaces. Academic Press, New York 1970. Dybin, V. B., and N. K. KarapetyantsGoogle Scholar
  24. [1]
    Rudin, W. eal and complex analysis. McGraw-Hill, New York 1970.Google Scholar
  25. [1]
    Coburn, L. A., and R. G. Douglas Translation operators on a half-line. Proc. Nat. Acad. Sci. USA 62, 1010–1013 (1969).MathSciNetMATHCrossRefGoogle Scholar
  26. [7]
    Duduchava, R. V. Integral equations with fixed singularities. Teubner-Texte zur Mathematik, Teubner, Leipzig 1979.Google Scholar
  27. [1]
    Rosenblum, M., and J. Rovnyak ardy classes and operator theory. Oxford Univ. Press, New York 1985.Google Scholar
  28. [7]
    Sarason, D. Function theory on the unit circle. Virginia Polytechnic Institute and State Univ., Blacks¬burg 1978.MATHGoogle Scholar
  29. [1]
    Berlin 1958. Garnett, J. B. Bounded analytic functions. Academic Press. New York 1981; Russian, transl.: Mir, Moscow 1984.Google Scholar
  30. [1]
    Lee, M., and D. Sarason The spectra of some Toeplitz operators. J. Math. Anal. Appl. 33, 529–543 (1971). Letterer, J.Google Scholar
  31. [1]
    Stegenga, D. A. Bounded Toeplitz operators on Hl and applications of the duality between Hl and the func¬tions of bounded mean oscillation. Amer. J. Math. 98: 3, 573–589 (1976).Google Scholar
  32. [1]
    Karlovich, Yu. I., and I. M. Spitkovski On the Fredholm property of certain singular integral operators with matrix coefficients of the class SAP and systems of convolution equations on a finite interval connected with them. Dokl. Akad. Nauk SSSR 269: 3, 531–535 (1983) Russian); also in: Soviet Math. Dokl. 27: 2, 358–363 (1983).Google Scholar
  33. [1]
    Schmeisser, 11.-J., and H. Triebel Topics in Fourier analysis and function spaces. Geest and Portig, Leipzig 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Albrecht Böttcher
    • 1
  • Bernd Silbermann
    • 1
  1. 1.Sektion Mathematik, Wissenschaftsbereich AnalysisTechnische Universität ChemnitzChemnitzGermany

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