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The concept of essential numerical range of an operator was dened and studied by Stamp i and Williams in 1972. Researchers generalised this idea of essential numerical range to a group of operators to the joint essential numerical range. In this paper, we consider the jointessential numerical range and show that the properties of the classical numerical range such as compactness also hold for the joint essential numerical range. Further, we show that the joint essential spectrum is contained in the joint essential numerical range by looking at the boundary of the joint essential spectrum.
Cambridge University Press, London-New York; 1973.
Dekker N. Joint numerical range and joint spectrum of Hilbert space operators. Ph.D. Thesis, University of Amsterdam; 1969.
Dash AT. Joint numerical range. Glasnik Mat. 1972;7:75-81.
Cyprian OS, Aywa S, Chikamai L. Some properties of the joint numerical range of the Aluthge transform. Int. J. of Pure and Applied Math. 2018;118(2):165-172.
Stampi JG, Williams JP. Growth condition and the numerical range in a Banach algebra. Tohoku Math. Journ. 1968;20:417-424.
Bonsall FF, Duncan J. Numerical Ranges of operators on Normed spaces and elements of Normed algebras, London Math. Soc. Lecture Notes series 2. Cambridge University Press, London-New York; 1971.
Au-Yeung YH, Tsing NK. An extension of the Hausdor-Toeplitz theorem on numerical range. Proc. Amer. Soc. 1983;89:215-218.
Lancaster JS. The boundary of the numerical range. Proc. Amer. Math. Soc. 1975;49:393-398.
Muller V. The joint essential numerical range, compact perturbations and the olsen problem. Studia Math. 2010;197:275-290.
Dash AT. Joint essential spectra. Pacic Journal of Mathematics. 1976;64:119-128.
Cyprian OS, Andrew Masibayi, Okelo NB. On the convexity of the joint essential numerical ranges. IJRDO. 2015;1:2328.
Cyprian OS. A note on the joint essential numerical range of Aluthge transform. Int. J. of Pure and Applied Math. 2018;118(3):573-579.
Dash AT. Joint spectra. Studia Math. 1973;45:225-237.