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Isomorphisms of Orlicz spaces

  • Seyyed Mohammad Tabatabaie EMAIL logo and Mahdi Latifpour
Published/Copyright: November 11, 2022
Forum Mathematicum
From the journal Forum Mathematicum Volume 35 Issue 1

Abstract

In this paper, we provide some isomorphism preserving conditions for (weighted) Orlicz spaces, and as a main result, it is proved that if there exist a bicontinuous linear operator T : L w 1 Φ ⁢ ( G 1 ) → L w 2 Φ ⁢ ( G 2 ) and a mapping a ↦ ( ξ ⁢ ( a ) , h ⁢ ( a ) ) from G 1 to ℂ × G 2 with T ⁢ λ a = ξ ⁢ ( a ) ⁢ λ h ⁢ ( a ) ⁢ T for all a ∈ G 1 , then G 1 and G 2 are isomorphic, where Φ is a Δ 2 -regular Young function, G 1 and G 2 are locally compact groups and w 1 and w 2 are weight functions. Also, for a class of Young functions Φ, we show that if C ⁢ V Φ ⁢ ( G 1 ) and CV Φ ⁢ ( G 2 ) are isometrically isomorphic, then G 1 and G 2 are isomorphic, CV Φ ⁢ ( G i ) is the space of all convolution operators on the Orlicz space L Φ ⁢ ( G i ) for i = 1 , 2 .

Keywords: Locally compact group; weighted Orlicz algebra; convolution operator; bipositive operator; biseparating operator; left multiplier
MSC 2010: 46E30; 43A22

Communicated by Siegfried Echterhoff

Acknowledgements

The authors would like to thank the referee of this paper for helpful remarks and suggestions to improve this paper.

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Received: 2022-02-11
Revised: 2022-08-30
Published Online: 2022-11-11
Published in Print: 2023-01-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Tameness of Margulis space-times with parabolics
  3. Sectoriality of degenerate elliptic operators via p-ellipticity
  4. Comparing Hecke eigenvalues of Siegel eigenforms
  5. Isomorphisms of Orlicz spaces
  6. The Engel graph of a finite group
  7. Nonnegative solutions of a fractional differential inequality on Grushin spaces and nilpotent Lie groups
  8. Representations of some associative pseudoalgebras
  9. On the convex components of a set in ℝ n
  10. Spectrality of homogeneous Moran measures on ℝ n
  11. Supercharacters of discrete algebra groups
  12. Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition
https://doi.org/10.1515/forum-2022-0051
Keywords for this article
Locally compact group; weighted Orlicz algebra; convolution operator; bipositive operator; biseparating operator; left multiplier

Articles in the same Issue

  1. Frontmatter
  2. Tameness of Margulis space-times with parabolics
  3. Sectoriality of degenerate elliptic operators via p-ellipticity
  4. Comparing Hecke eigenvalues of Siegel eigenforms
  5. Isomorphisms of Orlicz spaces
  6. The Engel graph of a finite group
  7. Nonnegative solutions of a fractional differential inequality on Grushin spaces and nilpotent Lie groups
  8. Representations of some associative pseudoalgebras
  9. On the convex components of a set in ℝ n
  10. Spectrality of homogeneous Moran measures on ℝ n
  11. Supercharacters of discrete algebra groups
  12. Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition
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