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1994 | 30 | 1 | 117-126
Tytuł artykułu

Hyperinvariant subspaces of operators on Hilbert spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
30
Numer
1
Strony
117-126
Opis fizyczny
Daty
wydano
1994
Twórcy
  • Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 84215 Bratislava, Slovakia
autor
  • Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, 81219 Bratislava, Slovakia
Bibliografia
  • [1] M. Barraa, Sous-espaces hyperinvariants d'un opérateur nilpotent sur un espace de Banach, J. Operator Theory 21 (1989), 315-321.
  • [2] M. Benlarbi Delaï et B. Charles, Description de Alg Lat A pour un opérateur A algébrique, Linear Algebra Appl. 187 (1993), 105-108.
  • [3] H. Bercovici, C₀-Fredholm operators II, Acta Sci. Math. (Szeged) 42 (1980), 3-42.
  • [4] H. Bercovici, Operator Theory and Arithmetic in $H^∞$, Math. Surveys Monographs 26, Providence, R.I., 1988.
  • [5] H. Bercovici, C. Foiaş and B. Sz.-Nagy, Reflexive and hyper-reflexive operators of class C₀, Acta Sci. Math. (Szeged) 43 (1981), 5-13.
  • [6] H. Bercovici and L. Kérchy, Quasisimilarity and properties of the commutant of $C_{11}$ contractions, ibid. 45 (1983), 67-74.
  • [7] L. Brickman and P. A. Fillmore, The invariant subspace lattice of a linear transformation, Canad. J. Math. 19 (1967), 810-822.
  • [8] J. B. Conway and P. Y. Wu, The splitting of Q(T₁ ⊕ T₂) and related questions, Indiana Univ. Math. J. 26 (1977), 41-56.
  • [9] J. A. Deddens, Every isometry is reflexive, Proc. Amer. Math. Soc. 28 (1971), 509-512.
  • [10] J. A. Deddens and P. A. Fillmore, Reflexive linear transformations, Linear Algebra Appl. 10 (1975), 89-93.
  • [11] R. G. Douglas, On the hyperinvariant subspaces for isometries, Math. Z. 107 (1968), 297-300.
  • [12] Š. Drahovský and M. Zajac, Hyperreflexive operators on finite dimensional Hilbert spaces, Math. Bohem. 118 (1993), 249-254.
  • [13] P. A. Fillmore, D. A. Herrero and W. F. Longstaff, The hyperinvariant subspace lattice of a linear transformation, Linear Algebra Appl. 17 (1977), 125-132.
  • [14] P. R. Halmos, Eigenvectors and adjoints, ibid. 4 (1971), 11-15.
  • [15] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.
  • [16] V. V. Kapustin, Reflexivity of operators: general methods and a criterion for almost isometric contractions, Algebra i Analiz 4 (2) (1992), 141-160 (in Russian); English transl.: St. Petersburg Math. J. 4 (1993), 319-335.
  • [17] V. V. Kapustin and A. V. Lipin, Operator algebras and invariant subspace lattices. I, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 178 (1989), 23-56 (in Russian).
  • [18] L. Kérchy, On the commutant of $C_{11}$-contractions, Acta Sci. Math. (Szeged) 43 (1981), 15-26.
  • [19] D. R. Larson and W. R. Wogen, Reflexivity properties of T ⊕ 0, J. Funct. Anal. 92 (1990), 448-467.
  • [20] S.-C. Ong, Remarks on invariant subspaces of finite dimensional operators, Linear Algebra Appl. 42 (1982), 99-101.
  • [21] S.-C. Ong, What kind of operators have few invariant subspaces?, ibid. 95 (1987), 181-185.
  • [22] S.-C. Ong, On equality of few invariant subspace lattices of operators, ibid. 144 (1991), 23-27.
  • [23] V. S. Shul'man, The Fuglede-Putnam theorem and reflexivity, Dokl. Akad. Nauk SSSR 210 (1973), 543-544 (in Russian); English transl.: Soviet Math. Dokl. 14 (1973), 784-786.
  • [24] S. O. Sickler, The invariant subspaces of almost unitary operators, Indiana Univ. Math. J. 24 (1975), 636-649.
  • [25] D. A. Suprunenko and R. I. Tyshkevich, Commutative Matrices, Nauka i Tekhnika, Minsk, 1966 (in Russian); English transl.: Academic Press, New York, 1968.
  • [26] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, and Akadémiai Kiadó, Budapest, 1970.
  • [27] K. Takahashi, Double commutants of operators quasi-similar to normal operators, Proc. Amer. Math. Soc. 92 (1984), 404-406.
  • [28] M. Uchiyama, Hyperinvariant subspaces of operators of class C₀(N), Acta Sci. Math. (Szeged) 39 (1977), 179-184.
  • [29] M. Uchiyama, Hyperinvariant subspaces for contractions of class $C_{·0}$, Hokkaido Math. J. 6 (1977), 260-272.
  • [30] P. Y. Wu, The hyperinvariant subspace lattice of the contraction of class $C_{·0}$, Proc. Amer. Math. Soc. 72 (1978), 527-530.
  • [31] P. Y. Wu, Hyperinvariant subspaces of $C_{11}$ contractions, ibid. 75 (1979), 53-58.
  • [32] P. Y. Wu, Hyperinvariant subspaces of $C_{11}$ contractions, II, Indiana Univ. Math. J. 27 (1978), 805-812.
  • [33] P. Y. Wu, Hyperinvariant subspaces of weak contractions, Acta Sci. Math. (Szeged) 41 (1979), 259-266.
  • [34] P. Y. Wu, Which linear transformations have isomorphic hyperinvariant subspace lattices?, Linear Algebra Appl. 169 (1992), 163-178.
  • [35] M. Zajac, Hyperinvariant subspace lattice of some C₀-contractions, Math. Slovaca 31 (1981), 397-404.
  • [36] M. Zajac, Hyperinvariant subspace lattice of weak contractions, ibid. 33 (1983), 75-80.
  • [37] M. Zajac, Hyperinvariant subspaces of weak contractions, in: Oper. Theory: Adv. Appl. 14, Birkhäuser, 1984, 291-299.
  • [38] M. Zajac, Hyperinvariant subspace lattice of isometries, Math. Slovaca 37 (1987), 291-297.
  • [39] M. Zajac, Hyperinvariant subspaces of weak contractions, II, in: Oper. Theory: Adv. Appl. 28, Birkhäuser, 1988, 317-322.
  • [40] M. Zajac, On the singular unitary part of a contraction, Rev. Roumaine Math. Pures Appl. 35 (1990), 379-384.
  • [41] M. Zajac, Hyper-reflexivity of isometries and weak contractions, J. Operator Theory 25 (1991), 43-51.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv30z1p117bwm
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