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1999 | 81 | 2 | 271-284
Tytuł artykułu

Wold decomposition of the Hardy space and Blaschke products similar to a contraction

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Języki publikacji
EN
Abstrakty
EN
The classical Wold decomposition theorem applied to the multiplication by an inner function leads to a special decomposition of the Hardy space. In this paper we obtain norm estimates for componentwise projections associated with this decomposition. An application to operators similar to a contraction is given.
Słowa kluczowe
Rocznik
Tom
81
Numer
2
Strony
271-284
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-10-29
poprawiono
1999-03-02
Twórcy
  • Department of Mathematics and Statistics, University at Albany, Albany, NY 12222, U.S.A.
Bibliografia
  • [1] P. R. Ahern and D. N. Clark, On inner functions with $B^p$ derivatives, Michigan Math. J. 23 (1976), 393-396.
  • [2] A. B. Aleksandrov, Multiplicity of boundary values of inner functions, Izv. Akad. Nauk Armyan. SSR Ser. Mat. 22 (1987), 490-503 (in Russian).
  • [3] A. B. Aleksandrov, Inner functions and related spaces of pseudocontinuable functions, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 170 (1989), 7-33 (in Russian); English transl.: J. Soviet Math. 63 (2) (1993).
  • [4] W. B. Arveson, Subalgebras of $C^*$-algebras, Acta Math. 123 (1969), 141-224.
  • [5] C. L. Belna, P. Colwell and G. Piranian, The radial limits of Blaschke products, Proc. Amer. Math. Soc. 93 (1985), 267-271.
  • [6] D. N. Clark, One dimensional perturbations of restricted shifts, J. Anal. Math. 25 (1972), 169-191.
  • [7] J. L. Doob, Measure Theory, Springer, New York, 1994.
  • [8] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933.
  • [9] P. R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102-112.
  • [10] T. L. Lance and M. I. Stessin, Multiplication invariant subspaces of Hardy spaces, Canad. J. Math. 49 (1997), 100-118.
  • [11] P. Lax, Translation invariant subspaces, Acta Math. 101 (1959), 163-178.
  • [12] V. Mascioni, Ideals of the disk algebra, operators related to Hilbert space contractions and complete boundedness, Houston J. Math. 20 (1994), 299-311.
  • [13] J. von Neumann, Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes, Math. Nachr. 4 (1950/51), 258-281.
  • [14] V. I. Paulsen, Every completely polynomially bounded operator is similar to a contraction, J. Funct. Anal. 55 (1984), 1-17.
  • [15] A. G. Poltoratski, The boundary behavior of pseudocontinuable functions, St. Petersburg Math. J. 5 (1994), 389-406.
  • [16] A. G. Poltoratski, On the distributions of the boundary values of Cauchy integrals, Proc. Amer. Math. Soc. 124 (1996), 2455-2463.
  • [17] W. Rudin, Boundary values of continuous analytic functions, ibid. 7 (1956), 808-811.
  • [18] W. Rudin, Function Theory in the Unit Ball of $C^n$, Springer, New York, 1980.
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Bibliografia
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bwmeta1.element.bwnjournal-article-cmv81i2p271bwm
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