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(ε, A)-approximate numerical radius orthogonality and numerical radius derivative

  • Jeet Sen and Kallol Paul EMAIL logo
Published/Copyright: February 15, 2023
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 73 Issue 1

Abstract

The purpose of this article is to study the notionof approximate numerical radius orthogonality in semi-Hilbertian structure. Given a positive operator A on a Hilbert space H , we introduce the notion of (ε, A)-approximate numerical radius orthogonality for A-bounded operators and characterize it. The results obtained here generalize all the existing notions of numerical radius orthogonality. Furthermore, for a fixed θ ∈ [0, 2π), we introduce the notion of numerical radius derivative DwAθ(T,S) of an A-bounded operator T in the direction of another A-bounded operator S and obtain a relation between DwAθ(T,S) and (ε, A)-approximate numerical radius orthogonality.

Keywords: Numerical radius orthogonality; A-numerical radius; compact operator; approximate Birkhoff-James orthogonality; numerical radius derivative, convex functions
MSC 2010: Primary 46B20; 46C50; 47C05; Secondary 47B65; 47L05

  1. (Communicated by Emanuel Chetcuti )

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Received: 2021-08-05
Accepted: 2022-03-24
Published Online: 2023-02-15
Published in Print: 2023-02-23

© 2023 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2023-0014
Keywords for this article
Numerical radius orthogonality; A-numerical radius; compact operator; approximate Birkhoff-James orthogonality; numerical radius derivative, convex functions

Articles in the same Issue

  1. RNDr. Stanislav Jakubec, DrSc. passed away
  2. Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means
  3. Conditions forcing the existence of relative complements in lattices and posets
  4. Radically principal MV-algebras
  5. A topological duality for dcpos
  6. Padovan or Perrin numbers that are concatenations of two distinct base b repdigits
  7. Addendum to “A generalization of a result on the sum of element orders of a finite group”
  8. Remarks on w-distances and metric-preserving functions
  9. Solution of logarithmic coefficients conjectures for some classes of convex functions
  10. Multiple periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian and partially periodic potentials
  11. Asymptotic stability of nonlinear neutral delay integro-differential equations
  12. On Catalan ideal convergent sequence spaces via fuzzy norm
  13. Fourier transform inversion: Bounded variation, polynomial growth, Henstock–Stieltjes integration
  14. (ε, A)-approximate numerical radius orthogonality and numerical radius derivative
  15. Wg-Drazin-star operator and its dual
  16. On the Lupaş q-transform of unbounded functions
  17. K-contact and (k, μ)-contact metric as a generalized η-Ricci soliton
  18. Compactness with ideals
  19. Number of cells containing a given number of particles in a generalized allocation scheme
  20. A new generalization of Nadarajah-Haghighi distribution with application to cancer and COVID-19 deaths data
  21. Compressive sensing using extropy measures of ranked set sampling
  22. A note on star partial order preservers on the set of all variance-covariance matrices
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