Publications Primitivity theorems for convolution algebras on McAlister monoids, Math. Proc. R. Ir. Acad. 114A (2014), 1 15. Finiteness and recognizability problems for substitution maps on two symbols, Semigroup Forum 81 (2010), no. 1, 71 84. On one-sided primitivity of Banach algebras, Proc. Edinb. Math. Soc. (2) 53 (2010), no. 1, 111 123. Algebras associated with a free inverse monoid, J. Aust. Math. Soc. 86 (2009), no. 1, 27 31. The contracted l 1 -algebra of a McAlister monoid, Math. Proc. R. Ir. Acad. 107 (2007), no. 1, 31 41. On the contracted l 1 -algebra of a polycyclic monoid, Port. Math. (N.S.) 63 (2006), no. 3, 327 334. A new prime C -algebra that is not primitive, J. Funct. Anal. 236 (2006), no. 2, 630 633. 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, 97 103. On the contracted l 1 -algebra of a 0-bisimple inverse semigroup, Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), no. 2, 285 295. Spectra in some inverse semigroup algebras, Math. Proc. R. Ir. Acad. 104A (2004), no. 2, 211 218. D.H. Luecking, C.M. McGregor, On the values of pi for norms on R 2, College Math. J. 35 (2004), no. 2, 84 92.
C.M. McGregor, Carleman s inequality, Amer. Math. Monthly 110 (2003), no. 5, 424 431. The extremal algebra on two Hermitians with square 1, Glasg. Math. J. 44 (2002), no. 2, 255 260. Some extremal algebras for Hermitians, Glasg. Math. J. 43 (2001), no. 1, 29 38. T.J. Ransford, Hermitian powers: a Müntz theorem and extremal algebras, Studia Math. 146 (2001), no. 1, 83 97. C.M. McGregor, Faithful, irreducible -representations for group algebras of free products, Proc. Edinburgh Math. Soc. (2) 42 (1999), no. 3, 559 574. Some inequalities for norm unitaries in Banach algebras, Proc. Edinburgh Math. Soc. (2) 21 (1978/79), no. 1, 17 23. On the l 1 -algebra of certain monoids, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 5, 1023 1031. H.G. Dales, Second-order cohomology groups of some semigroup algebras, Banach algebras 97 (Blaubeuren), 101 117, de Gruyter, Berlin, 1998. S. Bowling, First order cohomology of Banach semigroup algebras, Semigroup Forum 56 (1998), no. 1, 130 145. The centre of the algebra of a free inverse monoid, Semigroup Forum 55 (1997), no. 2, 215 220. M.A. Chaudhry, C.M. McGregor, The primitivity of semigroup algebras of free products, Semigroup Forum 54 (1997), no. 2, 221 229. 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, 939 945. 2
On the algebra of a free inverse monoid, J. Algebra 184 (1996), no. 1, 297 303 D. Khavinson, H. Shapiro, Rectangular parallelepipeds in ellipsoids, SIAM Rev. 38 (1996), no. 4, 655 657. Trace functions on the algebras of certain E-unitary inverse semigroups, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), no. 5, 1077 1084 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, 139 141. 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, 325 326. 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, 837 848. A.L.T. Paterson Amenability for discrete convolution semigroup algebras, Math. Scand. 66 (1990), no. 1, 141 146. J.M. Anderson, Duals of Banach spaces of entire functions, Glasgow Math. J. 32 (1990), no. 2, 215 220. A.L.T. Paterson C-algebras of Clifford semigroups, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 1-2, 129 145. C.M. McGregor, Polynomials in a Hermitian element, Glasgow Math. J. 30 (1988), no. 2, 171 176. 3
C.M. McGregor, Numerical ranges of powers of Hermitian elements, Glasgow Math. J. 28 (1986), no. 1, 37 45. A.L.T. Paterson C-algebras of inverse semigroups, Proc. Edinburgh Math. Soc. (2) 28 (1985), no. 1, 41 58. 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, 13 24. J.H. Williamson, Spectra of elements in the measure algebra of a free group, Proc. Roy. Irish Acad. Sect. A 82 (1982), no. 1, 109 120. Banach algebra. Report on the 70 s, prospects for the 80 s, Southeast Asian Bull. Math. 5 (1981), no. 1-2, 4 15. 46Hxx (01A65 46-02) F.F. Bonsall, Numerical ranges, Studies in functional analysis, pp. 1 49, MAA Stud. Math., 21, Math. Assoc. America, Washington, D.C., 1980. S.A.R. Hosseiniun, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), no. 3-4, 309 325. I.D. Macdonald, Some factorable nil rings of characteristic two, Proc. Roy. Soc. Edinburgh Sect. A 82 (1978/79), no. 3-4, 193 199. I. Namioka, Amenability of inverse semigroups and their semigroup algebras, Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), no. 3-4, 309 321. P.G. Spain, Commutators and normal operators, Glasgow Math. J. 18 (1977), no. 2, 197 198. The numerical range of an unbounded operator, Proc. Amer. Math. Soc. 55 (1976), no. 1, 95 96. C.M. McGregor, On the primitivity of the group ring of a free group, Bull. London Math. Soc. 8 (1976), no. 3, 294 298. 4
C.M. McGregor, A representation for l 1 (S), Bull. London Math. Soc. 8 (1976), no. 2, 156 160. P.J. Taylor, Norm inequalities for C -algebras, Proc. Roy. Soc. Edinburgh Sect. A 75 (1975/76), no. 2, 119 129. B.A. Barnes, The Banach algebra l 1 (S), J. Funct. Anal. 18 (1975), 96 113. A.M. Davie, von Neumann s inequality for Hilbert space operators, Bull. London Math. Soc. 7 (1975), 49 50. A.W. Tullo Finite dimensionality, nilpotents and quasinilpotents in Banach algebras, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), 45 49. Characterizations of commutativity for C -algebras, Glasgow Math. J. 15 (1974), 172 175. 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, 1973. vii+179 pp. Some extremal problems in the theory of numerical ranges, Acta Math. 128 (1972), no. 1-2, 123 142. Mapping theorems and the numerical radius, Proc. London Math. Soc. (3) 25 (1972), 486 502. A.M. Sinclair, On the boundary of the spatial numerical range, Bull. London Math. Soc. 4 (1972), 17 19. C.M. McGregor, Finite-dimensional normed linear spaces with numerical index 1, J. London Math. Soc. (2) 3 1971 717 721. 5
The powers of an operator of numerical radius one, Michigan Math. J. 18 1971 253 256. 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. 69 1971 79 85. Primitive idempotent measures on compact semigroups, Proc. Edinburgh Math. Soc. (2) 17 1970 95 103. The power inequality on normed spaces, Proc. Edinburgh Math. Soc. (2) 17 (1970/71), 237 240. C.M. McGregor, Operator norms determined by their numerical ranges, Proc. Edinburgh Math. Soc. (2) 17 (1970/71), 249 255. Some results on the numerical range of an operator, J. London Math. Soc. (2) 2 1970 741 745. Numerical range estimates for the norms of iterated operators, Glasgow Math. J. 11 1970 85 87. F.F. Bonsall, The spectral radius of a Hermitian element of a Banach algebra, Bull. London Math. Soc. 2 1970 178 180. C.M.McGregor, J.D. Pryce, A.J. White, The numerical index of a normed space, J. London Math. Soc. (2) 2 1970 481 488. The evaluation functionals associated with an algebra of bounded operators, Glasgow Math. J. 10 1969 73 76. S.T.L. Choy, B. Dummigan, On compact normal semigroups, Proc. Edinburgh Math. Soc. (2) 16 1968/1969 333 338. 6
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) 19 1968 97 111. F.F. Bonsall, Dual representations of Banach algebras, Acta Math. 117 1967 79 102. B modular annihilator algebras, Proc. Edinburgh Math. Soc. (2) 15 1966/1967 89 102. The continuity of the involution on Banach -algebras, J. London Math. Soc. 41 1966 701 706. 7