Book Review
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MathSciNet review:
1566346
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Book Information:
Author:
Henry Helson
Title:
Lectures on invariant subspaces
Additional book information:
Academic Press, New York, 1964. 11+130 pp. $5.00.
N. Aronszajn and K. T. Smith, Invariant subspaces of completely continuous operators, Ann. of Math. (2) 60 (1954), 345–350. MR 65807, DOI 10.2307/1969637
Allen R. Bernstein and Abraham Robinson, Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos, Pacific J. Math. 16 (1966), 421–431. MR 193504
Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019
M. S. Brodskiĭ, Triangular representation of some operators with completely continuous imaginary part, Soviet Math. Dokl. 1 (1960), 952–955. MR 0149288
M. S. Brodskiĭ and M. S. Livšic, Spectral analysis of non-self-adjoint operators and intermediate systems, Uspehi Mat. Nauk (N.S.) 13 (1958), no. 1(79), 3–85 (Russian). MR 0100793
Louis de Branges, Invariant subspaces of nonselfadjoint transformations, Bull. Amer. Math. Soc. 69 (1963), 587–590. MR 149290, DOI 10.1090/S0002-9904-1963-11008-3
Louis de Branges and James Rovnyak, The existence of invariant subspaces, Bull. Amer. Math. Soc. 70 (1964), 718–721. MR 161120, DOI 10.1090/S0002-9904-1964-11186-1
Louis de Branges and James Rovnyak, Correction to “The existence of invariant subspaces”, Bull. Amer. Math. Soc. 71 (1965), 396. MR 169024, DOI 10.1090/S0002-9904-1965-11312-X
Béla Sz.-Nagy and Ciprian Foiaş, Sur les contractions de l’espace de Hilbert. IX. Factorisations de la fonction caractéristique. Sous-espaces invariants, Acta Sci. Math. (Szeged) 25 (1964), 283–316 (French). MR 180871
Paul R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102–112. MR 152896, DOI 10.1515/crll.1961.208.102
P. R. Halmos, Invariant subspaces of polynomially compact operators, Pacific J. Math. 16 (1966), 433–437. MR 193505
Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
G. K. Kalisch, A functional anaysis proof of Titchmarsh’s theorem on convolution, J. Math. Anal. Appl. 5 (1962), 176–183. MR 140893, DOI 10.1016/S0022-247X(62)80002-X
Peter D. Lax, Translation invariant spaces, Acta Math. 101 (1959), 163–178. MR 105620, DOI 10.1007/BF02559553
P. D. Lax, Translation invariant spaces, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960) Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1961, pp. 299–306. MR 0140931
16. F. Riesz and M. Riesz, Über die Randwerte einer analytischen Funktion, Quatrième Congrès de Mathématiciens Scandinaves, Stockholm, 1916; pp. 27-44.
Gian-Carlo Rota, On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469–472. MR 112040, DOI 10.1002/cpa.3160130309
L. A. Sahnovič, A study of the “triangular form” of non-selfadjoint operators, Izv. Vysš. Učebn. Zaved. Matematika 1959 (1959), no. 4 (11), 141–149 (Russian). MR 0137001
Jack Schwartz, Subdiagonalization of operators in Hilbert space with compact imaginary part, Comm. Pure Appl. Math. 15 (1962), 159–172. MR 144212, DOI 10.1002/cpa.3160150205
- 1.
- N. Aronszajn and K. T. Smith, Invariant subspaces of completely continuous operators, Ann. of Math. (2) 60 (1954), 345-350. MR 0065807
- 2.
- A. R. Bernstein and A. Robinson, Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos, Pacific J. Math. 15 (1965), (to appear). MR 193504
- 3.
- A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239-255. MR 27954
- 4.
- M.S. Brodskiĭ, Triangular representations of some operators with completely continuous imaginary part, Soviet Math. Dokl. 1 (1961), 952-955. MR 149288
- 5.
- M. S. Brodskiĭ and M. S. Livshits, Spectral analysis of non-self-adjoint operators and intermediate systems, Uspehi Mat. Nauk 13 (1958), 3-85. (Russian) MR 100793
- 6.
- L. de Branges, Invariant subspaces of nonselfadjoint transformations, Bull. Amer. Math. Soc. 69 (1963), 587-590. MR 149290
- 7.
- L. de Branges and J. Rovnyak, The existence of invariant subspaces, Bull. Amer. Math. Soc. 70 (1964), 718-721. MR 161120
- 8.
- L. de Branges and J. Rovnyak, Correction to "The existence of invariant subspaces", Bull. Amer. Math. Soc. 71 (1965), 396. MR 169024
- 9.
- C. Foiaş and B. Sz.-Nagy, Sur les contractions de l'espace de Hilbert. IX. Factorisations de la fonction caractéristique. Sous espaces invariantes, Acta Sci. Math. (Szeged) 25 (1964), 283-316. MR 180871
- 10.
- P. R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102-112. MR 152896
- 11.
- P. R. Halmos, Invariant subspaces of polynomially compact operators, Pacific J. Math. 15 (1965), (to appear). MR 193505
- 12.
- K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 133008
- 13.
- G. K. Kalisch, A functional analysis proof of Titchmarsh's theorem on convolution, J. Math. Anal. Appl. 5 (1962), 176-183. MR 140893
- 14.
- P. D. Lax, Translation invariant spaces, Acta Math. 101 (1959), 163-178. MR 105620
- 15.
- P. D. Lax, Translation invariant spaces, Proc. Internat. Sympos. Linear Spaces, Jerusalem, 1960, pp. 299-306, Macmillan, New York, 1961. MR 140931
- 16.
- F. Riesz and M. Riesz, Über die Randwerte einer analytischen Funktion, Quatrième Congrès de Mathématiciens Scandinaves, Stockholm, 1916; pp. 27-44.
- 17.
- G. C. Rota, On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469-472. MR 112040
- 18.
- L. A. Sakhnovich, A study of the "triangular form" of non-selfadjoint operators, Izv. Vysš. Učebn. Zaved. Matematika 1959, no. 4 (11), 141-149. MR 137001
- 19.
- J. T. Schwartz, Subdiagonalization of operators in Hilbert space with compact imaginary part, Comm. Pure Appl. Math. 15 (1962), 159-172. MR 144212
Review Information:
Reviewer:
P. R. Halmos
Journal:
Bull. Amer. Math. Soc.
71 (1965), 490-494
DOI:
https://doi.org/10.1090/S0002-9904-1965-11294-0
