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The retraction of certain banach right modules associated to a character

  • Mahshid Dashti EMAIL logo and Sima Soltani Renani
Published/Copyright: July 19, 2019
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 69 Issue 4

Abstract

Let 𝓐 be a Banach algebra and let 𝓜 be a unital Banach algebra. For a homomorphism Φ from 𝓐 into 𝓜, we consider 𝓜 as a Banach right 𝓐-module and investigate when 𝓜 is a retract of 𝓐 with respect to Φ. We also give characterizations of admitting vector-valued invariant Φ-means in terms of projectivity and injectivity. Finally, we apply these results to abstract Segal algebras.

MSC 2010: 43A07; 46H05; 46L10
Keywords: Banach algebra; Banach module; homological property; retraction

  1. (Communicated by Emanuel Chetcuti)

Acknowledgement

The authors would like to express their deep gratitude to Professor Rasoul Nasr-Isfahani for his constant encouragements and guidance.

References

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Received: 2018-04-15
Accepted: 2018-11-19
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0260
Keywords for this article
Banach algebra; Banach module; homological property; retraction

Articles in the same Issue

  1. Regular papers
  2. On the finite embeddability property for quantum B-algebras
  3. A dual Ramsey theorem for finite ordered oriented graphs
  4. On EMV-Semirings
  5. A nonsymmetrical matrix and its factorizations
  6. On weakly 𝓗-permutable subgroups of finite groups
  7. The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions
  8. A geometrical version of Hardy-Rellich type inequalities
  9. On a Choquet-Stieltjes type integral on intervals
  10. Uniqueness of meromorphic functions sharing four small functions on annuli
  11. A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator
  12. Functions of bounded variation related to domains bounded by conic sections
  13. Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables
  14. Oscillatory criteria for the second order linear ordinary differential equations
  15. When deviation happens between rough statistical convergence and rough weighted statistical convergence
  16. The retraction of certain banach right modules associated to a character
  17. On sequence spaces generated by binomial difference operator of fractional order
  18. Some refinements of young type inequality for positive linear map
  19. On the Gromov-Hausdorff limit of metric spaces
  20. The beta exponentiated Nadarajah-Haghighi distribution: theory, regression model and application
  21. Hilbert algebras with supremum generated by finite chains
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