Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 34
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Akhtari, Fatemeh and Nasr-Isfahani, Rasoul 2014. Involutions on certain Banach algebras related to locally compact groups. Periodica Mathematica Hungarica, Vol. 68, Issue. 2, p. 143.

    Kosiek, Marek and Rudol, Krzysztof 2014. Dual Algebras and A-Measures. Journal of Function Spaces, Vol. 2014, p. 1.

    Laali, Javad 2014. The multipliers related products in Banach algebras. Quaestiones Mathematicae, Vol. 37, Issue. 4, p. 507.

    Mohammadi, S. M. and Laali, J. 2014. The Relationship between Two Involutive SemigroupsSandSTIs Defined by a Left MultiplierT. Journal of Function Spaces, Vol. 2014, p. 1.

    Abtahi, F. Amini, H. G. Lotfi, H. A. and Rejali, A. 2013. Some Intersections of the Weighted -Spaces. Abstract and Applied Analysis, Vol. 2013, p. 1.

    ABTAHI, FATEMEH 2013. Completely continuous and weakly completely continuous abstract Segal algebras. Proceedings - Mathematical Sciences, Vol. 123, Issue. 4, p. 539.

    Aghababa, Hasan Pourmahmood Shi, Luo Yi and Wu, Yu Jing 2013. Generalized notions of character amenability. Acta Mathematica Sinica, English Series, Vol. 29, Issue. 7, p. 1329.

    Hosseinioun, S. A. and Valadkhani, A. 2013. A semilattice structure for Arens products. Semigroup Forum, Vol. 87, Issue. 2, p. 428.

    ABTAHI, F. AMINI, H. G. LOTFI, H. A. and REJALI, A. 2012. AN ARBITRARY INTERSECTION OF Lp-SPACES. Bulletin of the Australian Mathematical Society, Vol. 85, Issue. 03, p. 433.

    Ghaffari, Ali 2012. On invariant convex subsets in algebras defined on a locally compact groupG. Studia Scientiarum Mathematicarum Hungarica, Vol. 49, Issue. 3, p. 301.

    Alaghmandan, Mahmood Nasr-Isfahani, Rasoul and Nemati, Mehdi 2010. On $${\phi}$$ -contractibility of the Lebesgue–Fourier algebra of a locally compact group. Archiv der Mathematik, Vol. 95, Issue. 4, p. 373.

    Galindo, Pablo Lindström, Mikael and Miralles, Alejandro 2009. Interpolating sequences on uniform algebras. Topology, Vol. 48, Issue. 2-4, p. 111.

    Shtern, A. I. 2009. Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture. Journal of Mathematical Sciences, Vol. 159, Issue. 5, p. 653.

    Rezavand, Reza Amini, Massoud Sattari, Mohammad Hossein and Ebrahimi Bagha, Davood 2008. Module Arens regularity for semigroup algebras. Semigroup Forum, Vol. 77, Issue. 2, p. 300.

    Mustafaev, G. S. 2007. On the radical for some class of Banach algebras. Functional Analysis and Its Applications, Vol. 41, Issue. 3, p. 241.

    Mustafaev, G. S. 2006. Regularity of Segal algebras. Functional Analysis and Its Applications, Vol. 40, Issue. 1, p. 62.

    Мустафаев, Г С and Mustafaev, H S 2006. О регулярности алгебры Сегала. Функциональный анализ и его приложения, Vol. 40, Issue. 1, p. 75.

    Мустафаев, Г С and Mustafaev, H S 2002. Банаховы алгебры с ограниченными группами образующих и свойство Шура. Математические заметки, Vol. 71, Issue. 5, p. 725.

    Cabello Sánchez, Félix and García, Ricardo 2001. Recent Progress in Functional Analysis, Proceedings of the International Functional Analysis Meeting on the Occasion of the 70th Birthday of Professor Manuel Valdivia.

    Baker, John Lau, Anthony To-Ming and Pym, John 1998. Module Homomorphisms and Topological Centres Associated with Weakly Sequentially Complete Banach Algebras. Journal of Functional Analysis, Vol. 158, Issue. 1, p. 186.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 84, Issue 3-4
  • January 1979, pp. 309-325

The second dual of a Banach algebra*

  • J. Duncan (a1) and S. A. R. Hosseiniun (a2)
  • DOI:
  • Published online: 14 November 2011

We give a survey of the current state of knowledge on the Arens second dual of a Banach algebra, including some simplified proofs of known results, some new results, some open problems and a full bibliography of the subject.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1F. E. Alexander .. The dual and bidual of certain A*-algebras. Proc. Amer. Math. Soc. 38 (1973), 571576.

4R. Arens . Operations induced in function classes. Monatsh. Math. 55 (1951), 119.

5R. Arens . The adjoint of a bilinear operation. Proc. Amer. Math. Soc. 2 (1951), 839848.

7M. C. F. Berglund . Ideal C*-algebras. Duke Math. J. 40 (1973), 241257.

10F. F. Bonsall and J. Duncan . Complete normed algebras (New York: Springer, 1973).

11P. Civin . Extensions of homomorphisms. Pacific J. Math. 11 (1961), 12231233.

13P. Civin . Annihilators in the second conjugate algebra of a group algebra. Pacific J. Math. 12 (1962), 855862.

14P. Civin and B. Yood . The second conjugate space of a Banach algebra as an algebra. Pacific J. Math. 11 (1961), 847870.

15I. G. Craw and N. J. Young . Regularity of multiplication in weighted group and semigroup algebras. Quart. J. Math. Oxford 25 (1974), 351358.

16J. W. Davenport . Multipliers on a Banach algebra with a bounded approximate identity. Pacific J. Math. 63 (1976), 131135.

19J. M. G. Fell . The dual spaces of Banach algebras. Trans. Amer. Math. Soc. 114 (1965), 227250.

21E. E. Granirer . The radical of L(G)*. Proc. Amer. Math. Soc. 41 (1973), 321324.

22S. L. Gulick . The bidual of a locally multiplicatively-convex algebra. Pacific J. Math. 17 (1966), 7196.

23S. L. Gulick . Commutativity and ideals in the biduals of topological algebras. Pacific J. Math. 18 (1966), 121137.

25J. Hennefeld . A note on the Arens product. Pacific J. Math. 26 (1968), 115119.

26J. Hennefeld . The Arens products and an embedding theorem. Pacific J. Math. 29 (1969), 551563.

28N. Macri . The continuity of Arens product on the Stone-Čech compactification of semigroups. Trans. Amer. Math. Soc. 191 (1974), 185193.

31S. A. McKilligan . Duality in B*-algebras. Proc. Amer. Math. Soc. 38 (1973), 8688.

32S. A. McKilligan . Arens regularity of certain Banach algebras which are ideals of a Banach algebra. Proc. Amer. Math. Soc. 50 (1975), 223229.

34T. W. Palmer . Arens multiplication and a characterization of W*-algebras. Proc. Amer. Math. Soc. 44 (1974), 8187.

37J. S. Pym . Convolution measure algebras are not usually Arens regular. Quart. J. Math. Oxford 25 (1974), 235240.

41J. D. Stafney . Arens multiplication and convolution. Pacific J. Math. 14 (1964), 14231447.

42Z. Takeda . Conjugate spaces of operator algebras. Proc. Japan Acad. 30 (1954), 9095.

44B. J. Tomiuk and P. K. Wong . The Arens product and duality in B*-algebras. Proc. Amer. Math. Soc. 25 (1970), 529535.

47P. K. Wong . The Arens product and duality in B*-algebras II. Proc. Amer. Math. Soc. 27 (1971), 535538.

48P. K. Wong . Modular annihilator A*-algebras. Pacific J. Math. 37 (1971), 825834.

49P. K. Wong . On the Arens product and annihilator algebras. Proc. Amer. Math. Soc. 30 (1971), 7983.

50P. K. Wong . On the Arens product and commutative Banach algebras. Proc. Amer. Math. Soc. 37 (1973), 111113.

51P. K. Wong . On the Arens product and certain Banach algebras. Trans. Amer. Math. Soc. 180 (1973), 437448.

52P. K. Wong . The second conjugate of certain Banach algebras. Canad. J. Math. 27 (1975), 10291035.

53P. K. Wong . A minimax formula for dual B*-algebras. Trans. Amer. Math. Soc. 224 (1976), 281289.

56N. J. Young . The irregularity of multiplication in group algebras. Quart. J. Math. Oxford 24 (1973), 5962.

60B. A. Barnes and J. Duncan . The Banach algebra l1(S). J. Functional Analysis 18 (1975), 96113.

61F. F. Bonsall and J. Duncan . Dually irreducible representations of Banach algebras. Quart. J. Math. Oxford 19 (1968), 97111.

64C. M. McGregor . A representation for l1(S). Bull. London Math. Soc. 8 (1976), 156160.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *