Dr Philip Spain
- Honorary Research Fellow (School of Mathematics & Statistics)
Publications
2017
Lampret, V. and Spain, P. G. (2017) How far is (1 + a/n)^n from e^a ? Working Paper. Researchgate.
Spain, P. G. (2017) The NC property for Banach algebras, and C^*-equivalence. Working Paper. Researchgate.
Spain, P. G. (2017) The Nonstraddling Lemma and a new look at the Heine-Borel Theorem. Working Paper. Researchgate.
Spain, P. G. (2017) Numerical range of a simple compression. Functional Analysis, Approximation and Computation, 9(1), pp. 25-35.
2016
Spain, P. G. (2016) Ultrahermitian Projections on Banach Spaces. Working Paper. Researchgate.
2015
Spain, P. G. (2015) Representations of C*-algebras in dual and right dual Banach algebras. Houston Journal of Mathematics, 41(1), pp. 231-263.
2013
Spain, P. G. (2013) Characterizations of Hilbert space and the Vidav-Palmer theorem. Rocky Mountain Journal of Mathematics, 43(4), pp. 1337-1354. (doi: 10.1216/RMJ-2013-43-4-1337)
2011
Spain, P. G. (2011) Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces. Proceedings of the Edinburgh Mathematical Society, 54(2), pp. 515-529. (doi: 10.1017/S0013091509000406)
2003
Dowson, H.R., Ghaemi, M.B. and Spain, P.G. (2003) Boolean algebras of projections and algebras of spectral operators. Pacific Journal of Mathematics, 209(1), pp. 1-16. (doi: 10.2140/pjm.2003.209.1)
Dowson, H.R., Ghaemi, M.B. and Spain, P.G. (2003) Boolean algebras of projections & algebras of spectral operators. Pacific Journal of Mathematics, 209, pp. 1-16.
2001
Spain, P. G. (2001) Unilaterally invertible normals are invertible. Quarterly Journal of Mathematics, 52(2), pp. 229-230. (doi: 10.1093/qjmath/52.2.229)
Spain, P. G. (2001) Order and square roots in hermitian Banach *-algebras. In: Kerchy, L., Foias, C. I., Gohberg, I. and Langer, H. (eds.) Recent Advances in Operator Theory and Related Topics: Bela Szokefalvi-Nagy Memorial Volume. Series: Operator theory, advances and applications (127). Birkhäuser Basel (Springer), pp. 561-584. ISBN 9783034895392 (doi: 10.1007/978-3-0348-8374-0_31)
2000
Albrecht, E. and Spain, P.G. (2000) When products of selfadjoints are normal. Proceedings of the American Mathematical Society, 128(8), pp. 2509-2511. (doi: 10.1090/S0002-9939-00-05830-5)
1996
Spain, P. G. (1996) Operator versions of the Kantorovich inequality. Proceedings of the American Mathematical Society, 124(9), pp. 2813-2819. (doi: 10.1090/S0002-9939-96-03424-7)
Spain, P. G. (1996) The Fermat point of a triangle. Mathematics Magazine, 69(2), pp. 131-133.
1995
Spain, P. G. (1995) Lipschitz2: a new version of an old principle. Bulletin of the London Mathematical Society, 27(6), pp. 565-566. (doi: 10.1112/blms/27.6.565)
Spain, P. G. (1995) A discrete variation on Kronecker's theorem. Linear Algebra and its Applications, 223-22, pp. 631-636. (doi: 10.1016/0024-3795(94)00340-J)
Spain, P. G. (1995) Tracking poles, representing Hankel operators, and the Nehari problem. Linear Algebra and its Applications, 223-24, pp. 637-694. (doi: 10.1016/0024-3795(94)00106-N)
Odoni, R. W. K. and Spain, P. G. (1995) Equidistribution of values of rational functions (mod p). Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 125(5), pp. 911-929. (doi: 10.1017/S0308210500022551)
1991
Spain, P. G. (1991) Best analytic approximation of rational functions of degree 2: symmetrization of formulae of N. J. Young. International Journal of Robust and Nonlinear Control, 1(1), pp. 43-45. (doi: 10.1002/rnc.4590010106)
1990
Helton, J. W., Spain, P. G. and Young, N. J. (1990) Tracking poles and representing Hankel operators directly from data. Numerische Mathematik, 58(1), pp. 641-660. (doi: 10.1007/BF01385646)
1978
Spain, P. G. (1978) Solving an operator equation by iteration. Linear Algebra and its Applications, 20(1), pp. 69-70. (doi: 10.1016/0024-3795(78)90030-7)
1977
Crabb, M. J. and Spain, P. G. (1977) Commutators and normal operators. Glasgow Mathematical Journal, 18(2), pp. 197-198. (doi: 10.1017/S001708950000327X)
Spain, P. G. (1977) Support projections on Banach spaces. Glasgow Mathematical Journal, 18(1), pp. 13-15. (doi: 10.1017/S0017089500002974)
1976
Spain, P.G. (1976) A generalisation of a theorem of Grothendieck. Quarterly Journal of Mathematics, 27(4), pp. 475-479. (doi: 10.1093/qmath/27.4.475)
Dowson, H. R., Gillespie, T. A. and Spain, P. G. (1976) A commutativity theorem for hermitian operators. Mathematische Annalen, 220(3), pp. 215-217. (doi: 10.1007/BF01431092)
1975
Spain, P. G. (1975) Boolean algebras of projections. Proceedings of the Edinburgh Mathematical Society, 19(03), p. 287. (doi: 10.1017/S001309150001556X)
1974
Spain, P. G. (1974) The decomposition of the dual of W*-algebra. Journal of the London Mathematical Society, s2-7(3), pp. 568-570. (doi: 10.1112/jlms/s2-7.3.568)
Spain, P. G. (1974) The W*-closure of a V*-algebra. Journal of the London Mathematical Society, s2-7(3), pp. 385-386. (doi: 10.1112/jlms/s2-7.3.385)
1972
Milner-White, E. J. and Spain, P. G. (1972) Quaternary structure of helical proteins with globular subunits. Biochemical Journal, 130(1), 17P. (doi: 10.1042/bj1300017Pa) (PMCID:PMC1174362)
Spain, P. G. (1972) On commutative V*-algebras II. Glasgow Mathematical Journal, 13(02), p. 129. (doi: 10.1017/S0017089500001531)
Spain, P. G. (1972) On well-bounded operators of type (B). Proceedings of the Edinburgh Mathematical Society, 18(01), p. 35. (doi: 10.1017/S0013091500026134)
Dowson, H. R. and Spain, P. G. (1972) An example in the theory of well-bounded operators. Proceedings of the American Mathematical Society, 32(1), p. 205. (doi: 10.1090/S0002-9939-1972-0288615-8)
1971
Spain, P. G. (1971) V*-algebras with weakly compact unit spheres. Journal of the London Mathematical Society, s2-4(1), pp. 62-64. (doi: 10.1112/jlms/s2-4.1.62)
Spain, P. G. (1971) On scalar-type spectral operators. Mathematical Proceedings of the Cambridge Philosophical Society, 69(03), p. 409. (doi: 10.1017/S0305004100046843)
1970
Spain, P. G. (1970) On commutative V*-algebras. Proceedings of the Edinburgh Mathematical Society, 17(02), p. 173. (doi: 10.1017/S0013091500009457)
Articles
Spain, P. G. (2017) Numerical range of a simple compression. Functional Analysis, Approximation and Computation, 9(1), pp. 25-35.
Spain, P. G. (2015) Representations of C*-algebras in dual and right dual Banach algebras. Houston Journal of Mathematics, 41(1), pp. 231-263.
Spain, P. G. (2013) Characterizations of Hilbert space and the Vidav-Palmer theorem. Rocky Mountain Journal of Mathematics, 43(4), pp. 1337-1354. (doi: 10.1216/RMJ-2013-43-4-1337)
Spain, P. G. (2011) Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces. Proceedings of the Edinburgh Mathematical Society, 54(2), pp. 515-529. (doi: 10.1017/S0013091509000406)
Dowson, H.R., Ghaemi, M.B. and Spain, P.G. (2003) Boolean algebras of projections and algebras of spectral operators. Pacific Journal of Mathematics, 209(1), pp. 1-16. (doi: 10.2140/pjm.2003.209.1)
Dowson, H.R., Ghaemi, M.B. and Spain, P.G. (2003) Boolean algebras of projections & algebras of spectral operators. Pacific Journal of Mathematics, 209, pp. 1-16.
Spain, P. G. (2001) Unilaterally invertible normals are invertible. Quarterly Journal of Mathematics, 52(2), pp. 229-230. (doi: 10.1093/qjmath/52.2.229)
Albrecht, E. and Spain, P.G. (2000) When products of selfadjoints are normal. Proceedings of the American Mathematical Society, 128(8), pp. 2509-2511. (doi: 10.1090/S0002-9939-00-05830-5)
Spain, P. G. (1996) Operator versions of the Kantorovich inequality. Proceedings of the American Mathematical Society, 124(9), pp. 2813-2819. (doi: 10.1090/S0002-9939-96-03424-7)
Spain, P. G. (1996) The Fermat point of a triangle. Mathematics Magazine, 69(2), pp. 131-133.
Spain, P. G. (1995) Lipschitz2: a new version of an old principle. Bulletin of the London Mathematical Society, 27(6), pp. 565-566. (doi: 10.1112/blms/27.6.565)
Spain, P. G. (1995) A discrete variation on Kronecker's theorem. Linear Algebra and its Applications, 223-22, pp. 631-636. (doi: 10.1016/0024-3795(94)00340-J)
Spain, P. G. (1995) Tracking poles, representing Hankel operators, and the Nehari problem. Linear Algebra and its Applications, 223-24, pp. 637-694. (doi: 10.1016/0024-3795(94)00106-N)
Odoni, R. W. K. and Spain, P. G. (1995) Equidistribution of values of rational functions (mod p). Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 125(5), pp. 911-929. (doi: 10.1017/S0308210500022551)
Spain, P. G. (1991) Best analytic approximation of rational functions of degree 2: symmetrization of formulae of N. J. Young. International Journal of Robust and Nonlinear Control, 1(1), pp. 43-45. (doi: 10.1002/rnc.4590010106)
Helton, J. W., Spain, P. G. and Young, N. J. (1990) Tracking poles and representing Hankel operators directly from data. Numerische Mathematik, 58(1), pp. 641-660. (doi: 10.1007/BF01385646)
Spain, P. G. (1978) Solving an operator equation by iteration. Linear Algebra and its Applications, 20(1), pp. 69-70. (doi: 10.1016/0024-3795(78)90030-7)
Crabb, M. J. and Spain, P. G. (1977) Commutators and normal operators. Glasgow Mathematical Journal, 18(2), pp. 197-198. (doi: 10.1017/S001708950000327X)
Spain, P. G. (1977) Support projections on Banach spaces. Glasgow Mathematical Journal, 18(1), pp. 13-15. (doi: 10.1017/S0017089500002974)
Spain, P.G. (1976) A generalisation of a theorem of Grothendieck. Quarterly Journal of Mathematics, 27(4), pp. 475-479. (doi: 10.1093/qmath/27.4.475)
Dowson, H. R., Gillespie, T. A. and Spain, P. G. (1976) A commutativity theorem for hermitian operators. Mathematische Annalen, 220(3), pp. 215-217. (doi: 10.1007/BF01431092)
Spain, P. G. (1975) Boolean algebras of projections. Proceedings of the Edinburgh Mathematical Society, 19(03), p. 287. (doi: 10.1017/S001309150001556X)
Spain, P. G. (1974) The decomposition of the dual of W*-algebra. Journal of the London Mathematical Society, s2-7(3), pp. 568-570. (doi: 10.1112/jlms/s2-7.3.568)
Spain, P. G. (1974) The W*-closure of a V*-algebra. Journal of the London Mathematical Society, s2-7(3), pp. 385-386. (doi: 10.1112/jlms/s2-7.3.385)
Milner-White, E. J. and Spain, P. G. (1972) Quaternary structure of helical proteins with globular subunits. Biochemical Journal, 130(1), 17P. (doi: 10.1042/bj1300017Pa) (PMCID:PMC1174362)
Spain, P. G. (1972) On commutative V*-algebras II. Glasgow Mathematical Journal, 13(02), p. 129. (doi: 10.1017/S0017089500001531)
Spain, P. G. (1972) On well-bounded operators of type (B). Proceedings of the Edinburgh Mathematical Society, 18(01), p. 35. (doi: 10.1017/S0013091500026134)
Dowson, H. R. and Spain, P. G. (1972) An example in the theory of well-bounded operators. Proceedings of the American Mathematical Society, 32(1), p. 205. (doi: 10.1090/S0002-9939-1972-0288615-8)
Spain, P. G. (1971) V*-algebras with weakly compact unit spheres. Journal of the London Mathematical Society, s2-4(1), pp. 62-64. (doi: 10.1112/jlms/s2-4.1.62)
Spain, P. G. (1971) On scalar-type spectral operators. Mathematical Proceedings of the Cambridge Philosophical Society, 69(03), p. 409. (doi: 10.1017/S0305004100046843)
Spain, P. G. (1970) On commutative V*-algebras. Proceedings of the Edinburgh Mathematical Society, 17(02), p. 173. (doi: 10.1017/S0013091500009457)
Book Sections
Spain, P. G. (2001) Order and square roots in hermitian Banach *-algebras. In: Kerchy, L., Foias, C. I., Gohberg, I. and Langer, H. (eds.) Recent Advances in Operator Theory and Related Topics: Bela Szokefalvi-Nagy Memorial Volume. Series: Operator theory, advances and applications (127). Birkhäuser Basel (Springer), pp. 561-584. ISBN 9783034895392 (doi: 10.1007/978-3-0348-8374-0_31)
Research Reports or Papers
Lampret, V. and Spain, P. G. (2017) How far is (1 + a/n)^n from e^a ? Working Paper. Researchgate.
Spain, P. G. (2017) The NC property for Banach algebras, and C^*-equivalence. Working Paper. Researchgate.
Spain, P. G. (2017) The Nonstraddling Lemma and a new look at the Heine-Borel Theorem. Working Paper. Researchgate.
Spain, P. G. (2016) Ultrahermitian Projections on Banach Spaces. Working Paper. Researchgate.