On Musielak-Orlicz spaces isometric to L2 or L∞.

Anna Kaminska

Collectanea Mathematica (1997)

  • Volume: 48, Issue: 4-5-6, page 563-569
  • ISSN: 0010-0757

Abstract

top
It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t) = c(t) u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented.

How to cite

top

Kaminska, Anna. "On Musielak-Orlicz spaces isometric to L2 or L∞.." Collectanea Mathematica 48.4-5-6 (1997): 563-569. <http://eudml.org/doc/40806>.

@article{Kaminska1997,
abstract = {It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t) = c(t) u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented.},
author = {Kaminska, Anna},
journal = {Collectanea Mathematica},
keywords = {Espacio de Orlicz; Funciones reales; Función de valor; Distribución ponderada; Espacios de Hilbert; Isometría; Operadores; Musiełak-Orlicz; surjective isometry; weighted composition operator},
language = {eng},
number = {4-5-6},
pages = {563-569},
title = {On Musielak-Orlicz spaces isometric to L2 or L∞.},
url = {http://eudml.org/doc/40806},
volume = {48},
year = {1997},
}

TY - JOUR
AU - Kaminska, Anna
TI - On Musielak-Orlicz spaces isometric to L2 or L∞.
JO - Collectanea Mathematica
PY - 1997
VL - 48
IS - 4-5-6
SP - 563
EP - 569
AB - It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t) = c(t) u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented.
LA - eng
KW - Espacio de Orlicz; Funciones reales; Función de valor; Distribución ponderada; Espacios de Hilbert; Isometría; Operadores; Musiełak-Orlicz; surjective isometry; weighted composition operator
UR - http://eudml.org/doc/40806
ER -

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.