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

M. Stessin

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 2, page 271-284
  • ISSN: 0010-1354

Abstract

top
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.

How to cite

top

Stessin, M.. "Wold decomposition of the Hardy space and Blaschke products similar to a contraction." Colloquium Mathematicae 81.2 (1999): 271-284. <http://eudml.org/doc/210739>.

@article{Stessin1999,
abstract = {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.},
author = {Stessin, M.},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {271-284},
title = {Wold decomposition of the Hardy space and Blaschke products similar to a contraction},
url = {http://eudml.org/doc/210739},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Stessin, M.
TI - Wold decomposition of the Hardy space and Blaschke products similar to a contraction
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 2
SP - 271
EP - 284
AB - 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.
LA - eng
UR - http://eudml.org/doc/210739
ER -

References

top
  1. [1] P. R. Ahern and D. N. Clark, On inner functions with B p derivatives, Michigan Math. J. 23 (1976), 393-396. 
  2. [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. [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). Zbl0761.30017
  4. [4] W. B. Arveson, Subalgebras of C * -algebras, Acta Math. 123 (1969), 141-224. 
  5. [5] C. L. Belna, P. Colwell and G. Piranian, The radial limits of Blaschke products, Proc. Amer. Math. Soc. 93 (1985), 267-271. Zbl0582.30022
  6. [6] D. N. Clark, One dimensional perturbations of restricted shifts, J. Anal. Math. 25 (1972), 169-191. Zbl0252.47010
  7. [7] J. L. Doob, Measure Theory, Springer, New York, 1994. 
  8. [8] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. Zbl0204.15001
  9. [9] P. R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math. 208 (1961), 102-112. Zbl0107.09802
  10. [10] T. L. Lance and M. I. Stessin, Multiplication invariant subspaces of Hardy spaces, Canad. J. Math. 49 (1997), 100-118. Zbl0879.47015
  11. [11] P. Lax, Translation invariant subspaces, Acta Math. 101 (1959), 163-178. Zbl0085.09102
  12. [12] V. Mascioni, Ideals of the disk algebra, operators related to Hilbert space contractions and complete boundedness, Houston J. Math. 20 (1994), 299-311. Zbl0819.46038
  13. [13] J. von Neumann, Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes, Math. Nachr. 4 (1950/51), 258-281. Zbl0042.12301
  14. [14] V. I. Paulsen, Every completely polynomially bounded operator is similar to a contraction, J. Funct. Anal. 55 (1984), 1-17. Zbl0557.46035
  15. [15] A. G. Poltoratski, The boundary behavior of pseudocontinuable functions, St. Petersburg Math. J. 5 (1994), 389-406. 
  16. [16] A. G. Poltoratski, On the distributions of the boundary values of Cauchy integrals, Proc. Amer. Math. Soc. 124 (1996), 2455-2463. Zbl0855.30032
  17. [17] W. Rudin, Boundary values of continuous analytic functions, ibid. 7 (1956), 808-811. Zbl0073.29701
  18. [18] W. Rudin, Function Theory in the Unit Ball of C n , Springer, New York, 1980. Zbl0495.32001

NotesEmbed ?

top

You must be logged in to post comments.