Research Article

Norm Properties of $S$-Universal Operators

Volume: 3 Number: 2 June 30, 2020
Joshua Muholo *, Job Bonyo
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Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences
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Norm Properties of $S$-Universal Operators

Abstract

We investigate the norm properties of a generalized derivation on a norm ideal $\mathcal{J}$ in $\mathcal{B}(H)$, the algebra of bounded linear operators on a Hilbert space $H$. Specifically, we extend the concept of $S-$universality from the inner derivation to the generalized derivation context, establish the necessary conditions for the attainment of the optimal value of the circumdiameters of numerical ranges and the spectra of two bounded linear operators on $H$. Moreover, we characterize the antidistance from an operator to its similarity orbit in terms of the circumdiameters, norms, numerical and spectra radii of a pair of $S$-universal operators.

Keywords

Spectrum, Numerical range, Circumdiameter, Similarity orbit, Antidistance, Norms;, Norm ideals, Normaloid, Spectraloid operators

Supporting Institution

MASENO UNIVERSITY

Thanks

I would like to thank the DergiPark for providing this platform for scholars and academia to submit their articles for publication.

References

  1. [1] J. G. Stampfli, The norm of a derivation, Pac. J. Math. 33 (1970).
  2. [2] R. Schatten, Norm ideals of completely continuos operators, Springler-Verlag,Berlin (1960),55-79.
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  4. [4] M. Barraa and M. Boumazgour, Inner derivation and norm equality, Proc. Amer. Math. Soc., 130(2) (2001), 471-476.
  5. [5] J. O. Bonyo and J. O. Agure, Norms of Derivations Implemented by S-universal Operators, Int. J. Math. Anal., 5(5) (2011), 215-222
  6. [6] J. O. Bonyo and J. O. Agure, Norms of Inner Derivations on Norm Ideals, Int. J. Math. Anal., 4 (14)(2010), 695-701.
  7. [7] F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag New York Heidelberg Berlin 1973.
  8. [8] A. Pere and M. Martin, Local Multipliers of $C^{*}-Algebras$Algebras, Springer-Verlag, Lodon New York Heidelberg Berlin.
  9. [9] S. Y. Shaw, On numerical ranges of generalized derivations and related properties, J. Austral. Math. Soc., 36 (1984), 134-142.
  10. [10] C. S. Lin,The Unilateral Shift and a Norm Equality for Bounded Linear Operators, Proc. Amer. Math. Soc., 127 (1999) No. 6, 1693-1696.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Publication Date

June 30, 2020

Submission Date

February 22, 2020

Acceptance Date

June 17, 2020

Published in Issue

Year 2020 Volume: 3 Number: 2

IZ

https://izlik.org/JA43SZ29AF

Cite

RIS / Bibtex
APA
Muholo, J., & Bonyo, J. (2020). Norm Properties of $S$-Universal Operators. Communications in Advanced Mathematical Sciences, 3(2), 82-90. https://izlik.org/JA43SZ29AF
AMA
1.Muholo J, Bonyo J. Norm Properties of $S$-Universal Operators. Communications in Advanced Mathematical Sciences. 2020;3(2):82-90. https://izlik.org/JA43SZ29AF
Chicago
Muholo, Joshua, and Job Bonyo. 2020. “Norm Properties of $S$-Universal Operators”. Communications in Advanced Mathematical Sciences 3 (2): 82-90. https://izlik.org/JA43SZ29AF.
EndNote
Muholo J, Bonyo J (June 1, 2020) Norm Properties of $S$-Universal Operators. Communications in Advanced Mathematical Sciences 3 2 82–90.
IEEE
[1]J. Muholo and J. Bonyo, “Norm Properties of $S$-Universal Operators”, Communications in Advanced Mathematical Sciences, vol. 3, no. 2, pp. 82–90, June 2020, [Online]. Available: https://izlik.org/JA43SZ29AF
ISNAD
Muholo, Joshua - Bonyo, Job. “Norm Properties of $S$-Universal Operators”. Communications in Advanced Mathematical Sciences 3/2 (June 1, 2020): 82-90. https://izlik.org/JA43SZ29AF.
JAMA
1.Muholo J, Bonyo J. Norm Properties of $S$-Universal Operators. Communications in Advanced Mathematical Sciences. 2020;3:82–90.
MLA
Muholo, Joshua, and Job Bonyo. “Norm Properties of $S$-Universal Operators”. Communications in Advanced Mathematical Sciences, vol. 3, no. 2, June 2020, pp. 82-90, https://izlik.org/JA43SZ29AF.
Vancouver
1.Joshua Muholo, Job Bonyo. Norm Properties of $S$-Universal Operators. Communications in Advanced Mathematical Sciences [Internet]. 2020 Jun. 1;3(2):82-90. Available from: https://izlik.org/JA43SZ29AF

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