J. Duncan, C.M. McGregor, Carleman s inequality, Amer. Math. Monthly 110 (2003), no. 5,

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1 Publications Primitivity theorems for convolution algebras on McAlister monoids, Math. Proc. R. Ir. Acad. 114A (2014), Finiteness and recognizability problems for substitution maps on two symbols, Semigroup Forum 81 (2010), no. 1, On one-sided primitivity of Banach algebras, Proc. Edinb. Math. Soc. (2) 53 (2010), no. 1, Algebras associated with a free inverse monoid, J. Aust. Math. Soc. 86 (2009), no. 1, The contracted l 1 -algebra of a McAlister monoid, Math. Proc. R. Ir. Acad. 107 (2007), no. 1, On the contracted l 1 -algebra of a polycyclic monoid, Port. Math. (N.S.) 63 (2006), no. 3, A new prime C -algebra that is not primitive, J. Funct. Anal. 236 (2006), no. 2, C.M. McGregor, W.D. Munn, A property of the complex semigroup algebra of a free monoid, J. Aust. Math. Soc. 81 (2006), no. 1, On the contracted l 1 -algebra of a 0-bisimple inverse semigroup, Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), no. 2, Spectra in some inverse semigroup algebras, Math. Proc. R. Ir. Acad. 104A (2004), no. 2, D.H. Luecking, C.M. McGregor, On the values of pi for norms on R 2, College Math. J. 35 (2004), no. 2,

2 C.M. McGregor, Carleman s inequality, Amer. Math. Monthly 110 (2003), no. 5, The extremal algebra on two Hermitians with square 1, Glasg. Math. J. 44 (2002), no. 2, Some extremal algebras for Hermitians, Glasg. Math. J. 43 (2001), no. 1, T.J. Ransford, Hermitian powers: a Müntz theorem and extremal algebras, Studia Math. 146 (2001), no. 1, C.M. McGregor, Faithful, irreducible -representations for group algebras of free products, Proc. Edinburgh Math. Soc. (2) 42 (1999), no. 3, Some inequalities for norm unitaries in Banach algebras, Proc. Edinburgh Math. Soc. (2) 21 (1978/79), no. 1, On the l 1 -algebra of certain monoids, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 5, H.G. Dales, Second-order cohomology groups of some semigroup algebras, Banach algebras 97 (Blaubeuren), , de Gruyter, Berlin, S. Bowling, First order cohomology of Banach semigroup algebras, Semigroup Forum 56 (1998), no. 1, The centre of the algebra of a free inverse monoid, Semigroup Forum 55 (1997), no. 2, M.A. Chaudhry, C.M. McGregor, The primitivity of semigroup algebras of free products, Semigroup Forum 54 (1997), no. 2, C.M. McGregor, W.D. Munn, A.S. Wassermann, On the algebra of a free monoid, Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), no. 5,

3 On the algebra of a free inverse monoid, J. Algebra 184 (1996), no. 1, D. Khavinson, H. Shapiro, Rectangular parallelepipeds in ellipsoids, SIAM Rev. 38 (1996), no. 4, Trace functions on the algebras of certain E-unitary inverse semigroups, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), no. 5, Comment, Amer. Math. Monthly 102 (1995), no. 3, 194. C.M. McGregor, The Arens irregularity of an extremal algebra, Proc. Edinburgh Math. Soc. (2) 37 (1994), no. 1, C.M. McGregor, Interpolation and inequalities for functions of exponential type: the Arens irregularity of an extremal algebra, Glasgow Math. J. 35 (1993), no. 3, Notes, Amer. Math. Monthly 100 (1993), no. 1, 59. A. Ülger, Almost periodic functionals on Banach algebras, Rocky Mountain J. Math. 22 (1992), no. 3, A.L.T. Paterson Amenability for discrete convolution semigroup algebras, Math. Scand. 66 (1990), no. 1, J.M. Anderson, Duals of Banach spaces of entire functions, Glasgow Math. J. 32 (1990), no. 2, A.L.T. Paterson C-algebras of Clifford semigroups, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 1-2, C.M. McGregor, Polynomials in a Hermitian element, Glasgow Math. J. 30 (1988), no. 2,

4 C.M. McGregor, Numerical ranges of powers of Hermitian elements, Glasgow Math. J. 28 (1986), no. 1, A.L.T. Paterson C-algebras of inverse semigroups, Proc. Edinburgh Math. Soc. (2) 28 (1985), no. 1, J.B. Conway, A.L.T. Paterson, Monogenic inverse semigroups and their C -algebras, Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), no. 1-2, J.H. Williamson, Spectra of elements in the measure algebra of a free group, Proc. Roy. Irish Acad. Sect. A 82 (1982), no. 1, Banach algebra. Report on the 70 s, prospects for the 80 s, Southeast Asian Bull. Math. 5 (1981), no. 1-2, Hxx (01A ) F.F. Bonsall, Numerical ranges, Studies in functional analysis, pp. 1 49, MAA Stud. Math., 21, Math. Assoc. America, Washington, D.C., S.A.R. Hosseiniun, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), no. 3-4, I.D. Macdonald, Some factorable nil rings of characteristic two, Proc. Roy. Soc. Edinburgh Sect. A 82 (1978/79), no. 3-4, I. Namioka, Amenability of inverse semigroups and their semigroup algebras, Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), no. 3-4, P.G. Spain, Commutators and normal operators, Glasgow Math. J. 18 (1977), no. 2, The numerical range of an unbounded operator, Proc. Amer. Math. Soc. 55 (1976), no. 1, C.M. McGregor, On the primitivity of the group ring of a free group, Bull. London Math. Soc. 8 (1976), no. 3,

5 C.M. McGregor, A representation for l 1 (S), Bull. London Math. Soc. 8 (1976), no. 2, P.J. Taylor, Norm inequalities for C -algebras, Proc. Roy. Soc. Edinburgh Sect. A 75 (1975/76), no. 2, B.A. Barnes, The Banach algebra l 1 (S), J. Funct. Anal. 18 (1975), A.M. Davie, von Neumann s inequality for Hilbert space operators, Bull. London Math. Soc. 7 (1975), A.W. Tullo Finite dimensionality, nilpotents and quasinilpotents in Banach algebras, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), Characterizations of commutativity for C -algebras, Glasgow Math. J. 15 (1974), F.F. Bonsall, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York, Heidelberg, Berlin 1973, x+301 pp. F.F. Bonsall, Numerical ranges. II, London Mathematical Society Lecture Notes Series, No. 10. Cambridge University Press, New York-London, vii+179 pp. Some extremal problems in the theory of numerical ranges, Acta Math. 128 (1972), no. 1-2, Mapping theorems and the numerical radius, Proc. London Math. Soc. (3) 25 (1972), A.M. Sinclair, On the boundary of the spatial numerical range, Bull. London Math. Soc. 4 (1972), C.M. McGregor, Finite-dimensional normed linear spaces with numerical index 1, J. London Math. Soc. (2)

6 The powers of an operator of numerical radius one, Michigan Math. J F.F. Bonsall, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Mathematical Society Lecture Note Series, 2 Cambridge University Press, London-New York 1971 iv+142 pp. Compact operators and Banach algebras, Proc. Cambridge Philos. Soc Primitive idempotent measures on compact semigroups, Proc. Edinburgh Math. Soc. (2) The power inequality on normed spaces, Proc. Edinburgh Math. Soc. (2) 17 (1970/71), C.M. McGregor, Operator norms determined by their numerical ranges, Proc. Edinburgh Math. Soc. (2) 17 (1970/71), Some results on the numerical range of an operator, J. London Math. Soc. (2) Numerical range estimates for the norms of iterated operators, Glasgow Math. J F.F. Bonsall, The spectral radius of a Hermitian element of a Banach algebra, Bull. London Math. Soc C.M.McGregor, J.D. Pryce, A.J. White, The numerical index of a normed space, J. London Math. Soc. (2) The evaluation functionals associated with an algebra of bounded operators, Glasgow Math. J S.T.L. Choy, B. Dummigan, On compact normal semigroups, Proc. Edinburgh Math. Soc. (2) /

7 The elements of complex analysis, John Wiley & Sons, London-New York-Sydney 1968 ix+313 pp. F.F. Bonsall, Dually irreducible representations of Banach algebras, Quart. J. Math. Oxford Ser. (2) F.F. Bonsall, Dual representations of Banach algebras, Acta Math B modular annihilator algebras, Proc. Edinburgh Math. Soc. (2) / The continuity of the involution on Banach -algebras, J. London Math. Soc