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Volume 26 - October 1983

Contents

Page 3 of 4

Research Article

  • The duals of generic space curves and complete intersections

  • J. W. Bruce
  • Published online by Cambridge University Press:
    20 January 2009, pp. 259-263
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  • In a previous paper we discussed the duals of generic hypersurfaces: both smooth hypersurfaces in ℝn and algebraic hypersurfaces in real or complex projective space ℙn. In this note we show how to extend the methods of [1] to cover the case of complete intersections in ℙn and preface this with a brief discussion on the contact of space curves in ℝn with planes. We shall use the notation of [1].

Book Reviews

Research Article

  • In which metric spaces are parallel bodies of closed sets closed?

  • Gerald Beer
  • Published online by Cambridge University Press:
    20 January 2009, pp. 265-273
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  • Let X be a metric space with metric d and for each x in X let Bλ[x] denote the closed ball of radius λ about x. Following Valentine [15] if K⊂X and λ is positive, then we call the set Bλ[K]=∪x∈KBλ[x] the λ-parallel body of K. The following fact is obvious.

Book Reviews

  • H. Matsumura, Commutative Algebra, Second Edition (Benjamin/Cummings, 1980), 313 pp., $19.50.

  • L. O'Carroll
  • Published online by Cambridge University Press:
    20 January 2009, pp. 114-115
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  • T. A. Whitelaw, An Introduction to Linear Algrbra, (Blackie, 1983), ix + 241 pp., £7·95 (paper covers).

  • H. G. Anderson
  • Published online by Cambridge University Press:
    20 January 2009, pp. 396-397
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  • E. B. Davies, One-Parameter Semigroups (Academic Press, London, 1980), viii + 230 pp., £19.80.

  • R. J. Archbold
  • Published online by Cambridge University Press:
    20 January 2009, pp. 115-116
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Research Article

  • A sharpening of the Berkson-Glickfeld theorem

  • Zoltan Magyar
  • Published online by Cambridge University Press:
    20 January 2009, pp. 275-278
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  • It is known that if in a Banach*-algebra with unit the following holds:

    then it is a C*-algebra (see [3]).

    We shall show that the above theorem can be sharpened in the following way: we replace the submultiplicativity of the norm by the weaker assumption

    Observe that under this assumption even the existence of exp(ih) is not at all obvious, but it will be proved to be true below. Our main result is Theorem 2 which depends on Theorem 1. Our last remark is the equivalent-norm-version of the statement.

Obituary

  • Obituary

  • F. Bath, W.L. Edge
  • Published online by Cambridge University Press:
    20 January 2009, pp. 279-281
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Book Reviews

  • R. D. Richtmyer, Principles of advanced mathematical physics, Volume II (Springer-Verlag, 1981), xii + 322 pp., DM72.

  • D. J. Wallace
  • Published online by Cambridge University Press:
    20 January 2009, pp. 397-398
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  • L. W. Beineke and R. J. Wilson (eds.), Selected topics in graph theory (Academic Press, 1979), pp. 451, £34·40.

  • I. Anderson
  • Published online by Cambridge University Press:
    20 January 2009, p. 398
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  • P. Billingsley, Probability and measure (Wiley, 1979), pp. 532, £28·95.

  • Gavin Brown
  • Published online by Cambridge University Press:
    20 January 2009, pp. 398-399
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  • C.-H. Sah, Hilbert's third problem: scissors congruence (Pitman, 1979), pp. 240, £9·95.

  • Elmer Rees
  • Published online by Cambridge University Press:
    20 January 2009, pp. 399-400
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Page 3 of 4