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92 M. KARAMANLIS AND P. J. PSARRAKOS
References
[1] G. Birkhoff, Orthogonality in linear metric spaces, Duke Math. J. 1 (1935), 169–172.
[2] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Mathematical Society Lecture Note Series,
Cambridge University Press, New York, 1971.
[3] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Mathematical Society Lec-
ture Notes Series, Cambridge University Press, New York, 1973.
[4] J. Chmielinski, On an ε-Birkhoff orthogonality, J. Ineq. Pure and Appl. Math. 6 (2005),
Article 79.
[5] Ch. Chorianopoulos, S. Karanasios and P. Psarrakos, A definition of numerical range of
rectangular matrices, Linear Multilinear Algebra 57 (2009), 459–475.
[6] Ch. Chorianopoulos and P. Psarrakos, Birkhoff-James approximate orthogonality sets
and numerical ranges, Linear Algebra Appl. 434 (2011), 2089–2108.
[7] S. S. Dragomir, On approximation of continuous linear functionals in normed linear
spaces, An. Univ. Timi¸soara Ser. S¸tiin¸t. Mat. 29 (1991), 51–58.
[8] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press,
Cambridge, 1991.
[9] R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer.
Math. Soc. 61 (1947), 265–292.
[10] J. G. Stampfli and J. P. Williams, Growth conditions and the numerical range in a
Banach algebra, Tˆohoku Math. Journ. 20 (1968), 417–424.
(M. Karamanlis and P. J. Psarrakos) Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece E-mail address: kararemilt@gmail.com, ppsarr@math.ntua.gr

