IJPAM: Volume 112, No. 4 (2017)

Title

ON THE MAXIMAL NUMERICAL RANGE
OF ELEMENTARY OPERATORS

Authors

Flora Mati Runji$^1$, John Ogonji Agure$^2$, Fredrick Oluoch Nyamwala$^3$
$^1$Department of Mathematics, Statistics and Actuarial Sciences
Karatina University
P.O. Box 1957-10101, Karatina, KENYA
$^2$Department of Pure and Applied Mathematics
Maseno University
P.O. Box 333, Maseno, KENYA
$^3$Department of Mathematics and Physics
Moi University
P.O. Box 3900-30100, Eldoret, KENYA

Abstract

The notion of the numerical range has been generalized in different directions. One such direction, is the maximal numerical range introduced by Stampfli (1970) to derive an identity for the norm of a derivation on $L(H)$. Unlike the other generalizations, the maximal numerical range has not been largely explored by researchers as many only refer to it in their quest to determine the norm of operators. In this paper we establish how the algebraic maximal numerical range of elementary operators is related to the closed convex hull of the maximal numerical range of the implementing operators $ A=\left(A_{1}, A_{2},..., A_{n}\right)$, $B=\left(B_{1}, B_{2},..., B_{n}\right)$, on the algebra of bounded linear operators on a Hilbert space $H$. The results obtained are an extension of the work done by Seddik [2] and Fong [9].

History

Received: October 24, 2016
Revised: December 8, 2016
Published: February 19, 2017

AMS Classification, Key Words

AMS Subject Classification: 47A12, 47B47
Key Words and Phrases: algebraic maximal numerical range, elementary operator

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How to Cite?

DOI: 10.12732/ijpam.v112i4.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 4
Pages: 741 - 747


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