Isometries of Musielak-Orlicz spaces II

J. Jamison; A. Kamińska; Pei-Kee Lin

Studia Mathematica (1993)

  • Volume: 104, Issue: 1, page 75-89
  • ISSN: 0039-3223

Abstract

top
A characterization of isometries of complex Musielak-Orlicz spaces L Φ is given. If L Φ is not a Hilbert space and U : L Φ → L Φ is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all f ∈ L Φ . Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.

How to cite

top

Jamison, J., Kamińska, A., and Lin, Pei-Kee. "Isometries of Musielak-Orlicz spaces II." Studia Mathematica 104.1 (1993): 75-89. <http://eudml.org/doc/215960>.

@article{Jamison1993,
abstract = {A characterization of isometries of complex Musielak-Orlicz spaces $L_Φ$ is given. If $L_Φ$ is not a Hilbert space and $U : L_Φ → L_Φ$ is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all $f ∈ L_Φ$. Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.},
author = {Jamison, J., Kamińska, A., Lin, Pei-Kee},
journal = {Studia Mathematica},
keywords = {isometries of complex Musielak-Orlicz spaces; surjective isometry; regular set isomorphism; real Nakano spaces},
language = {eng},
number = {1},
pages = {75-89},
title = {Isometries of Musielak-Orlicz spaces II},
url = {http://eudml.org/doc/215960},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Jamison, J.
AU - Kamińska, A.
AU - Lin, Pei-Kee
TI - Isometries of Musielak-Orlicz spaces II
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 1
SP - 75
EP - 89
AB - A characterization of isometries of complex Musielak-Orlicz spaces $L_Φ$ is given. If $L_Φ$ is not a Hilbert space and $U : L_Φ → L_Φ$ is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all $f ∈ L_Φ$. Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.
LA - eng
KW - isometries of complex Musielak-Orlicz spaces; surjective isometry; regular set isomorphism; real Nakano spaces
UR - http://eudml.org/doc/215960
ER -

References

top
  1. [1] S. Banach, Theory of Linear Operations, North-Holland, 1987. Zbl0613.46001
  2. [2] E. Berkson and H. Porta, Hermitian operators and one-parameter groups of isometries in Hardy spaces, Trans. Amer. Math. Soc. 185 (1973), 331-344. Zbl0278.46024
  3. [3] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge University Press, 1971. Zbl0207.44802
  4. [4] R. Fleming and J. E. Jamison, Isometries on certain Banach spaces, J. London Math. Soc. (2) 9 (1974), 363-371. Zbl0288.47027
  5. [5] R. Fleming, J. E. Jamison and A. Kamińska, Isometries of Musielak-Orlicz spaces, in: Proceedings of the Conference on Function Spaces, Edwardsville 1990, Marcel Dekker, 1992, 139-154. Zbl0769.46018
  6. [6] J. E. Jamison and I. Loomis, Isometries of Orlicz spaces of vector valued functions, Math. Z. 193 (1986), 363-371. 
  7. [7] N. J. Kalton and G. V. Wood, Orthonormal systems in Banach spaces and their applications, Math. Proc. Cambridge Philos. Soc. 79 (1976), 493-510. Zbl0327.46022
  8. [8] A. Kamińska, Some convexity properties of Musielak-Orlicz spaces of Bochner type, Rend. Circ. Mat. Palermo (2) Suppl. 10 (1985), 63-73. Zbl0609.46015
  9. [9] A. Kamińska, Isometries of Orlicz spaces equipped with the Orlicz norm, Rocky Mountain J. Math., to appear. Zbl0834.46019
  10. [10] W. Kozlowski, Modular Function Spaces, Marcel Dekker, New York 1988. Zbl0661.46023
  11. [11] M. A. Krasnosel'skiǐ and Ya. B. Rutickiǐ, Convex Functions and Orlicz Spaces, Noordhoff, Groningen 1961. 
  12. [12] G. Lumer, On the isometries of reflexive Orlicz spaces, Ann. Inst. Fourier (Grenoble) 13 (1) (1963), 99-109. Zbl0189.43201
  13. [13] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, 1983. 
  14. [14] H. Nakano, Topology and Linear Spaces, Nihonbashi, Tokyo 1951. 
  15. [15] A. R. Sourour, The isometries of L p ( Ω , X ) , J. Funct. Anal. 30 (1978), 276-285. Zbl0396.47020
  16. [16] M. G. Zaǐdenberg, Groups of isometries of Orlicz spaces, Soviet Math. Dokl. 17 (1976), 432-436. Zbl0345.46028
  17. [17] M. G. Zaǐdenberg, On isometric classification of symmetric spaces, ibid. 18 (1977), 636-640. Zbl0381.46016

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.