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Linear derivations on Banach *-algebras

  • Husain Alhazmi and Abdul Nadim Khan EMAIL logo
Published/Copyright: January 29, 2021
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 71 Issue 1

Abstract

In this paper, it is shown that there is no positive integer n such that the set of x∈A for which [(xδ)n,(x∗δ)n(xδ)n]∈Z(A), where δ is a linear derivation on A or there exists a central idempotent e∈Q such that δ=0 on eQ and (1−e)Q satisfies S4(X1, X2, X3, X4). Moreover, we establish other related results.

Keywords: Banach *-algebra; linear derivation
MSC 2010: Primary 16W25; 46J45

  1. (Communicated by Emanuel Chetcuti)

Acknowledgement

The authors wishes to thank the referee/s for helpful comments and suggestions. This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (G:148/662/1439). The authors, therefore, gratefully acknowledge the DSR technical and financial support.

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Received: 2019-10-13
Accepted: 2020-06-30
Published Online: 2021-01-29
Published in Print: 2021-02-23

© 2021 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0450
Keywords for this article
Banach *-algebra; linear derivation

Articles in the same Issue

  1. Regular papers
  2. Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
  3. Doc. RNDr. Roman Frič, DrSc. passed away
  4. Outer and inner approximations in quantum spaces
  5. Linear derivations on Banach *-algebras
  6. New fractional order discrete Grüss type inequality
  7. Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
  8. Generalized Minkowski type inequality for pseudo-integral
  9. Study of the Q-spiral-like functions of complex order
  10. Radius of starlikeness of certain analytic functions
  11. Successive approximations for a differential equation in a Banach space via Constantin condition
  12. Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
  13. Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
  14. Sequence selection properties in Cp(X) with the double ideals
  15. On the paranormed Nörlund difference sequence space of fractional order and geometric properties
  16. On certain Diophantine equations concerning the area of right triangles
  17. Weighted projective Ricci curvature in Finsler geometry
  18. Euler classes of vector bundles over manifolds
  19. A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
  20. Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
  21. The (α, β)-ramification invariants of a number field
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