Rocky Mountain Journal of Mathematics

Multipliers in locally convex *-algebras

Marina Haralampidou, Lourdes Palacios, and Carlos J. Signoret Poillon

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We consider a complete locally $m$-convex $^*$-algebra with continuous involution, which is also a ``perfect'' projective limit, and describe its multiplier algebra, {under a weaker topology}, making it a locally $C^*$-algebra. The same is applied in the case of certain locally convex $H^*$-algebras.

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Rocky Mountain J. Math., Volume 43, Number 6 (2013), 1931-1940.

First available in Project Euclid: 25 February 2014

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Zentralblatt MATH identifier

Primary: 46H05: General theory of topological algebras 46H10: Ideals and subalgebras 46K05: General theory of topological algebras with involution

Preannihilator algebra locally $m$-convex $H*$-algebra locally $C*$-algebra Arens-Michael decomposition left (right) multiplier multiplier algebra perfect projective system perfect topological algebra


Haralampidou, Marina; Palacios, Lourdes; Poillon, Carlos J. Signoret. Multipliers in locally convex *-algebras. Rocky Mountain J. Math. 43 (2013), no. 6, 1931--1940. doi:10.1216/RMJ-2013-43-6-1931.

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  • C. Apostol, $b^{\ast }$-algebras and their representation, J. Lond. Math. Soc. 3 (1971), 30-38.
  • G.F. Bachelis and J.W. McCoy, Left centralizers of an $H^*$-algebra, Proc. Amer. Math. Soc. 43 (1974), 106-110.
  • F.T. Birtel, Banach algebras of multipliers, Duke Math. J. 28 (1961), 203-211.
  • N. Bourbaki, Théorie des ensembles, Chapt. 3, Hermann, Paris, 1967.
  • W.M. Ching and J.S.W. Wong, Multipliers and $ H^{\ast }$-algebras, Pac. J. Math. 22 (1967), 387-396.
  • A. El Kinani, On locally pre-$C^{\ast }$-algebra structures in locally $m$-convex $H^{\ast }$-algebras, Turk. J. Math. 26 (2002), 263-271.
  • M. Haralampidou, On locally $H^{\ast }$-algebras, Math. Jap. 38 (1993), 451-460.
  • –––, Annihilator topological algebras, Port. Math. 51 (1994), 147-162.
  • –––, The Krull nature of locally $C^{\ast } $-algebras, Contemp. Math. 328, American Mathematical Society, Providence, RI, 2003.
  • –––, Centralizers on certain complemented topological algebras, in preparation.
  • J. Horváth, Topological vector spaces and distributions, Vol. I, Addison-Wesley Publ. Co., Reading, MA, 1966.
  • T. Husain, Multipliers of topological algebras, Diss. Math. 285 (1989).
  • A. Inoue, Locally $C^{\ast }$-algebras, Mem. Fac. Sci. Kyushu Univ. 25 (1971), 197-235.
  • D.L. Johnson and C.D. Lahr, Multipliers and derivations of Hilbert algebras, Math. Japon. 25 (1980), 43-54.
  • M. Joiţa, On bounded module maps between Hilbert modules over locally $C^{\ast }$-algebras, Acta Math. Univ. Com. 74 (2005), 71-78.
  • G. Köthe, Topological vector spaces, I, Springer-Verlag, Berlin, 1969.
  • R. Larsen, The multiplier problem, Lect. Notes Math. 105, Springer-Verlag, Berlin, 1969.
  • –––, Introduction to the theory of multipliers, Grundl. Math. Wiss. 175, Springer-Verlag, Berlin 1971.
  • A. Mallios, Topological algebras. Selected topics, North-Holland, Amsterdam, 1986.
  • E.A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952), (reprinted 1968).
  • Noor Mohammad, On compact multipliers of topological algebras, Per. Math. Hungar. 32 (1996), 209-212.
  • M.A. Naĭmark, Normed algebras, Wolters-Noordhoff Publishers, Groningen, 1972.
  • N.C. Phillips, Inverse limits of $C^*$-algebras, J. Oper. Theor. 19 (1988), 159-195.
  • Z. Sebestyén, Every $C^{\ast }$-seminorm is automatically submultiplicative, Per. Math. Hungar. 10 (1979), 1-8.
  • Ju-Kwei Wang, Multipliers of commutative Banach algebras, Pac. J. Math. 11 (1961), 1131-1149.
  • J. Weinder, Topological invariants for generalized operator algebras, Ph.D. thesis, Heidelberg, 1987. \noindentstyle