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On the amenability of a class of Banach algebras with application to measure algebra

  • Mohammad Reza Ghanei EMAIL logo und Mehdi Nemati
Veröffentlicht/Copyright: 5. Oktober 2019
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 69 Heft 5

Abstract

Let 𝓛 be a Lau algebra and X be a topologically invariant subspace of 𝓛* containing UC(𝓛). We prove that if 𝓛 has a bounded approximate identity, then strict inner amenability of 𝓛 is equivalent to the existence of a strictly inner invariant mean on X. We also show that when 𝓛 is inner amenable the cardinality of the set of topologically left invariant means on 𝓛* is equal to the cardinality of the set of topologically left invariant means on RUC(𝓛). Applying this result, we prove that if 𝓛 is inner amenable and 〈𝓛2〉 = 𝓛, then the essential left amenability of 𝓛 is equivalent to the left amenability of 𝓛. Finally, for a locally compact group G, we consider the measure algebra M(G) to study strict inner amenability of M(G) and its relation with inner amenability of G.

MSC 2010: Primary 46H05; Secondary 43A07; 43A10
Keywords: inner amenability; Lau algebra; left amenability; mixed identity; measure algebra; strict inner amenability

This research for the first author was in part supported by a grant from IPM (No. 94470067).

  1. (Communicated by Emanuel Chetcuti)

References

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Received: 2018-09-14
Accepted: 2019-01-29
Published Online: 2019-10-05
Published in Print: 2019-10-25

© 2019 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Regular papers
  2. Professor Anatolij Dvurečenskij
  3. A generating theorem of punctured surface triangulations with inner degree at least 4
  4. Natural extension of EF-spaces and EZ-spaces to the pointfree context
  5. On weak isometries in directed groups
  6. On self-injectivity of the f-ring Frm(𝓟(ℝ), L)
  7. On the extensions of discrete valuations in number fields
  8. On certain classes of generalized derivations
  9. Nilpotent elements in medial semigroups
  10. Power of meromorphic function sharing polynomials with derivative of it’s combination with it’s shift
  11. Sharp coefficient bounds for starlike functions associated with the Bell numbers
  12. Sufficient conditions for Carathéodory functions and applications to univalent functions
  13. Blending type approximation by complex SzĂĄsz-Durrmeyer-Chlodowsky operators in compact disks
  14. Linear directional differential equations in the unit ball: solutions of bounded L-index
  15. On oscilatory fourth order nonlinear neutral differential equations – IV
  16. Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms
  17. Lerch’s theorem on nabla time scales
  18. IK-convergence of sequences of functions
  19. Convolution theorems related with the solvability of Wiener-Hopf plus Hankel integral equations and Shannon’s sampling formula
  20. Stabilization of third order differential equation by delay distributed feedback control with unbounded memory
  21. On the amenability of a class of Banach algebras with application to measure algebra
  22. A bivariate Kumaraswamy-exponential distribution with application
  23. Berry-Esseen bounds for wavelet estimator in time-varying coefficient models with censored dependent data
  24. Corrigendum to ”on the congruent number problem over integers of cyclic number fields”, Math. Slovaca 66(3) (2016), 561–564
https://doi.org/10.1515/ms-2017-0299
Schlagwörter fĂŒr diesen Artikel
inner amenability; Lau algebra; left amenability; mixed identity; measure algebra; strict inner amenability

Artikel in diesem Heft

  1. Regular papers
  2. Professor Anatolij Dvurečenskij
  3. A generating theorem of punctured surface triangulations with inner degree at least 4
  4. Natural extension of EF-spaces and EZ-spaces to the pointfree context
  5. On weak isometries in directed groups
  6. On self-injectivity of the f-ring Frm(𝓟(ℝ), L)
  7. On the extensions of discrete valuations in number fields
  8. On certain classes of generalized derivations
  9. Nilpotent elements in medial semigroups
  10. Power of meromorphic function sharing polynomials with derivative of it’s combination with it’s shift
  11. Sharp coefficient bounds for starlike functions associated with the Bell numbers
  12. Sufficient conditions for Carathéodory functions and applications to univalent functions
  13. Blending type approximation by complex SzĂĄsz-Durrmeyer-Chlodowsky operators in compact disks
  14. Linear directional differential equations in the unit ball: solutions of bounded L-index
  15. On oscilatory fourth order nonlinear neutral differential equations – IV
  16. Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms
  17. Lerch’s theorem on nabla time scales
  18. IK-convergence of sequences of functions
  19. Convolution theorems related with the solvability of Wiener-Hopf plus Hankel integral equations and Shannon’s sampling formula
  20. Stabilization of third order differential equation by delay distributed feedback control with unbounded memory
  21. On the amenability of a class of Banach algebras with application to measure algebra
  22. A bivariate Kumaraswamy-exponential distribution with application
  23. Berry-Esseen bounds for wavelet estimator in time-varying coefficient models with censored dependent data
  24. Corrigendum to ”on the congruent number problem over integers of cyclic number fields”, Math. Slovaca 66(3) (2016), 561–564
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