Invertible and normal composition operators on the Hilbert Hardy space of a half–plane

Valentin Matache

Concrete Operators (2016)

  • Volume: 3, Issue: 1, page 77-84
  • ISSN: 2299-3282

Abstract

top
Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.

How to cite

top

Valentin Matache. "Invertible and normal composition operators on the Hilbert Hardy space of a half–plane." Concrete Operators 3.1 (2016): 77-84. <http://eudml.org/doc/277103>.

@article{ValentinMatache2016,
abstract = {Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.},
author = {Valentin Matache},
journal = {Concrete Operators},
keywords = {Composition operator; Hardy space; Half–plane; composition operator; half-plane},
language = {eng},
number = {1},
pages = {77-84},
title = {Invertible and normal composition operators on the Hilbert Hardy space of a half–plane},
url = {http://eudml.org/doc/277103},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Valentin Matache
TI - Invertible and normal composition operators on the Hilbert Hardy space of a half–plane
JO - Concrete Operators
PY - 2016
VL - 3
IS - 1
SP - 77
EP - 84
AB - Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.
LA - eng
KW - Composition operator; Hardy space; Half–plane; composition operator; half-plane
UR - http://eudml.org/doc/277103
ER -

References

top
  1. [1] Bourdon P. S., Matache V., Shapiro J. H., On convergence to the Denjoy-Wolff point, Illinois J. Math. 49 (2005), no. 2, 405-430.  Zbl1088.30015
  2. [2] Bourdon P. S., Narayan S. K., Normal weighted composition operators on the Hardy space H2.U/, J. Math. Anal. Appl. 367(2010), 278-286.  Zbl1195.47013
  3. [3] Cowen, C. C., Ko, E., Hermitian weighted composition operators on H2, Trans. Amer. Math. Soc., 362(2010), no. 11, 5771-5801.  Zbl1213.47034
  4. [4] Duren P., Theory of Hp Spaces, Pure and Applied Mathematics, Vol. 38 Academic Press, New York–London 1970.  
  5. [5] Elliott S., Jury M. T., Composition operators on Hardy spaces of a half-plane, Bull. Lond. Math. Soc. 44 (2012), no. 3, 489-495.  Zbl1248.47025
  6. [6] Gunatillake G., Invertible weighted composition operators, J. Funct. Anal. 261 (2011), no. 3, 831-860.  Zbl1218.47037
  7. [7] Hoffman K., Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1962.  
  8. [8] Hyvarinen O., Lindstrom M., Nieminen I., Saukko E., Spectra of weighted composition operators with automorphic symbols, J. Funct. Anal. 265 (2013), 1749-1777.  Zbl1325.47054
  9. [9] Matache V., Composition operators on Hp of the upper half-plane, An. Univ. Timis¸oara Ser. S¸ tiin¸t. Mat. 27 (1989), no. 1, 63-66.  Zbl0791.47031
  10. [10] Matache V., Notes on hypercyclic operators, Acta Sci. Math. (Széged) 58(1993), no. 1-4, 401-410.  Zbl0795.47002
  11. [11] Matache V., Composition operators on Hardy spaces of a half-plane, Proc. Amer. Math. Soc. 127 (1999), no. 5, 1483-1491.  Zbl0916.47022
  12. [12] Matache V., Weighted composition operators on H2 and applications, Complex Anal. Oper. Theory 2 (2008), no. 1, 169-197.  Zbl1158.47019
  13. [13] Matache V., Numerical ranges of composition operators with inner symbols, Rocky Mountain J. Math. 42(2012), no. 1, 235-249.  Zbl1244.47004
  14. [14] Matache V., Isometric weighted composition operators, New York J. Math. 20(2014), 711-726.  Zbl1298.47037
  15. [15] Nordgren E. A., Composition operators, Canad. J. Math. 20(1968), 442-449.  Zbl0161.34703

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.