Spectra of subnormal Hardy type operators

K. Rudol

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 3, page 213-222
  • ISSN: 0066-2216

Abstract

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The essential spectrum of bundle shifts over Parreau-Widom domains is studied. Such shifts are models for subnormal operators of special (Hardy) type considered earlier in [AD], [R1] and [R2]. By relating a subnormal operator to the fiber of the maximal ideal space, an application to cluster values of bounded analytic functions is obtained.

How to cite

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K. Rudol. "Spectra of subnormal Hardy type operators." Annales Polonici Mathematici 65.3 (1997): 213-222. <http://eudml.org/doc/270014>.

@article{K1997,
abstract = {The essential spectrum of bundle shifts over Parreau-Widom domains is studied. Such shifts are models for subnormal operators of special (Hardy) type considered earlier in [AD], [R1] and [R2]. By relating a subnormal operator to the fiber of the maximal ideal space, an application to cluster values of bounded analytic functions is obtained.},
author = {K. Rudol},
journal = {Annales Polonici Mathematici},
keywords = {subnormal operators; Hardy classes; function algebras; essential spectrum; bundle shifts over Parreau-Widom; fiber of the maximal ideal space},
language = {eng},
number = {3},
pages = {213-222},
title = {Spectra of subnormal Hardy type operators},
url = {http://eudml.org/doc/270014},
volume = {65},
year = {1997},
}

TY - JOUR
AU - K. Rudol
TI - Spectra of subnormal Hardy type operators
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 3
SP - 213
EP - 222
AB - The essential spectrum of bundle shifts over Parreau-Widom domains is studied. Such shifts are models for subnormal operators of special (Hardy) type considered earlier in [AD], [R1] and [R2]. By relating a subnormal operator to the fiber of the maximal ideal space, an application to cluster values of bounded analytic functions is obtained.
LA - eng
KW - subnormal operators; Hardy classes; function algebras; essential spectrum; bundle shifts over Parreau-Widom; fiber of the maximal ideal space
UR - http://eudml.org/doc/270014
ER -

References

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  1. [AD] M. B. Abrahamse and R. G. Douglas, A class of subnormal operators related to multiply connected domains, Adv. in Math. 19 (1976), 106-148. Zbl0321.47019
  2. [AK] M. B. Abrahamse and T. Kriete, The spectral multiplicity of a multiplication operator, Indiana Univ. Math. J. 22 (1973), 845-857. Zbl0259.47031
  3. [C] J. B. Conway, Subnormal Operators, Pitman, Boston, 1981. 
  4. [C1] J. B. Conway, Spectral properties of certain operators on Hardy spaces of planar domains, Integral Equations Operator Theory 10 (1987), 659-706. Zbl0658.47028
  5. [Cu] J. Cufi, H ∞ + C in several variables, Collect. Math. 23 (1982), 109-123. 
  6. [G] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. Zbl0213.40401
  7. [G1] T. W. Gamelin, Iversen's Theorem and fiber algebras, Pacific J. Math. 46 (1973), 389-414. Zbl0237.46059
  8. [M] W. Mlak, Szegő measures related to plane sets, Comment. Math., Tomus spec. in honorem L. Orlicz 1 (1978), 239-249. Zbl0445.46037
  9. [R] K. Rudol, On spectral mapping theorems, J. Math. Anal. Appl. 97 (1983), 131-139. Zbl0526.47006
  10. [R0] K. Rudol, Spectral mapping theorems for analytic functional calculi, in: Adv. in Invariant Subspaces and Other Results of Operator Theory, R. G. Douglas et al. (eds.), Oper. Theory: Adv. Appl. 17, Birkhäuser, 1986, 331-340. 
  11. [R1] K. Rudol, The generalised Wold Decomposition for subnormal operators, Integral Equations Operator Theory 11 (1988), 420-436. 
  12. [R2] K. Rudol, Subnormal operators of Hardy type, in: Banach Center Publ. 38, Inst. Math., Polish Acad. Sci., 1997, 315-324. 
  13. [S] M. V. Samokhin, Some classical problems of analytic functions theory in Parreau-Widom domains, Mat. Sb. 182 (1991), 892-910 (in Russian). Zbl0761.30020
  14. [S1] M. V. Samokhin, On limit properties of bounded holomorphic functions and maximum modulus principle in domains of arbitrary connectivity, Mat. Sb. 135 (1988), 497-513 (in Russian). Zbl0663.30028
  15. [W] H. Widom, H p sections of vector bundles over Riemann surfaces, Ann. of Math. 94 (1971), 304-324. Zbl0238.32014

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