Skip to main content
SpringerLink
Log in

Five problems on invariant subspaces

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. J. Wermer, “The existence of invariant subspaces,” Duke Math. J.,19, No. 4, 615–622 (1952).

    Google Scholar 

  2. Yu. I. Lyubich and V. I. Matsaev, “On operators with a separable spectrum,” Matem. Sb.,56(98), No. 4, 433–468 (1962).

    Google Scholar 

  3. A. S. Markus, L. N. Nikol'skii, and N. K. Nikol'skii, “Unitary spectrum of a contraction in Banach space,” Journal of Soviet Mathematics,2, No. 2, 112 (1974).

    Google Scholar 

  4. E. Bishop, “Spectral theory for operators in Banach space,” Trans. Amer. Math. Soc.,86, 414–445 (1957).

    Google Scholar 

  5. P. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, New Jersey (1967).

    Google Scholar 

  6. A. Brown and P. R. Halmos, “Algebraic properties of Toeplitz operators,” J. reine u angew. Math.,213, No. 1–2, 89–101 (1963).

    Google Scholar 

  7. B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators in Hilbert Space [Russian translation], Mir, Moscow (1970).

    Google Scholar 

  8. I. Ts. Gokhberg and M. Krein, The Theory of Volterra Operators in Hilbert Space and Its Applications. Translations of Mathematical Monographs, Vol. 24, American Mathematical Society, Providence, R. I. (1970).

    Google Scholar 

  9. V. P. Khavin, “Spaces of Analytic Functions,” in: Progress in Mathematics, Vol. 1, Mathematical Analysis, Plenum Press, New York, 76–167 (1968).

    Google Scholar 

  10. M. Altman, “Invariant subspaces of completely continuous operators in locally convex linear topological spaces,” Studia Math.,15, No. 2, 129–130 (1956).

    Google Scholar 

  11. A. L. Shields, “A note on invariant subspaces,” Mich. Math. J.,17, No. 3, 231–233 (1970).

    Google Scholar 

  12. P. R. Halmos, “Invariant subspaces of polynomially compact operators,” Pacif. J. Math.,16, 433–437 (1966).

    Google Scholar 

  13. D. Deckart, R. G. Douglas, and C. Pearcy, “On invariant subspaces of quasitriangular operators,” Amer. J. Math.,91, No. 3, 637–647 (1969).

    Google Scholar 

  14. J. Bram, “Subnormal operators,” Duke Math. J.,22, 75–94 (1955).

    Google Scholar 

  15. I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Non-self-adjoint Operators, Translations of Mathematical Monographs, Vol. 8, American Mathematical Society, Providence, R. I. (1969).

    Google Scholar 

  16. N. K. Nikol'skii, “On spectral analysis on a unitary spectrum. Point spectrum,” Dokl. Akad. Nauk SSSR,199, No. 3, 544–547 (1971).

    Google Scholar 

  17. A. S. Markus, “A problem of spectral synthesis for operators with a point spectrum,” Izv. Akad. Nauk, Ser. Matem.,34, No. 3, 662–688 (1970).

    Google Scholar 

  18. J. Wermer, “On invariant subspaces of normal operators,” Proc. Amer. Math. Soc.,3, No. 2, 270–277 (1952).

    Google Scholar 

  19. L. A. Rubel and A. L. Shields, “The space of bounded analytic functions on a region,” Ann. Inst. Fourier,16, No. 1, 238–277 (1966).

    Google Scholar 

  20. D. Sarason, “Weak-star density of polynomials,” preprint.

  21. S. G. Mikhlin, The Numerical Realization of Variational Methods [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  22. J. S. Byrnes and D. J. Newman, “Completeness preserving multipliers,” Proc. Amer. Math. Soc.,21, No. 2, 445–450 (1969).

    Google Scholar 

  23. H. Helson and G. Szego, “A problem in prediction theory,” Ann. Mat. Pure Appl.,51, 107–138 (1960).

    Google Scholar 

  24. H. Helson and D. Sarason, “Past and future,” Math. Scand.,21, 5–16 (1967).

    Google Scholar 

  25. N. K. Nikol'skii, “Spectral synthesis and the problem of weight approximation in some spaces of analytic functions increasing close to the boundary,” Izv. Akad. Nauk Arm. SSR, Ser. Matem.,6, No. 5, 345–367 (1971).

    Google Scholar 

  26. N. K. Nikol'skii, “A multiple translation with a simple spectrum,” Seminars in Mathematics, Vol. 19, Consultants Bureau, New York, (1972).

    Google Scholar 

  27. B. Sz.-Nagy and C. Foias, “Complements á l'etude des opérateurs de class C0, Acta Sci. Math.,31, No. 3–4, 287–296 (1970).

    Google Scholar 

  28. A. K. Kitover, “Spectral properties of unitary operators in C space,” Journal of Soviet Mathematics,2, No. 2, 99 (1974).

    Google Scholar 

  29. J. I. Ginsberg and D. J. Newman, “Generators of Certain radical algebras,” J. Approx. Theory,3, No. 3, 229–236 (1970).

    Google Scholar 

  30. A. Beurling, “On two problems concerning linear transformations in Hilbert spaces,” Acta Math.,81, No. 1–2, 239–255 (1949).

    Google Scholar 

  31. Y. Domar, “Spectral analysis in spaces of sequences summable with weights,” J. Func. Anal.,5, No. 1, 1–13 (1970).

    Google Scholar 

  32. N. K. Nikol'skii, “On spaces and algebras of Toeplitz matrices which act in ℓp,” Sibirsk. Matem. Zh.,7, No. 1, 146–158 (1966).

    Google Scholar 

Download references

Authors
  1. N. K. Nikol'skii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 23, pp. 115–127, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikol'skii, N.K. Five problems on invariant subspaces. J Math Sci 2, 441–450 (1974). https://doi.org/10.1007/BF01099001

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01099001

Keywords

Search

Navigation