Annals of Functional Analysis

φ-contractibility and character contractibility of Fréchet algebras

Fatemeh Abtahi and Somaye Rahnama

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Right φ-contractibility and right character contractibility of Banach algebras have been introduced and investigated. Here, we introduce and generalize these concepts for Fréchet algebras. We then verify available results about right φ-contractibility and right character contractibility of Banach algebras for Fréchet algebras. Moreover, we provide related results about Segal–Fréchet algebras.

Article information

Ann. Funct. Anal., Volume 8, Number 1 (2017), 75-89.

Received: 15 January 2016
Accepted: 24 June 2016
First available in Project Euclid: 31 October 2016

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Zentralblatt MATH identifier

Primary: 46H05: General theory of topological algebras
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46A03: General theory of locally convex spaces 46A04: Locally convex Fréchet spaces and (DF)-spaces

abstract Segal algebra Fréchet algebra right character contractibility right $\varphi$-contractibility


Abtahi, Fatemeh; Rahnama, Somaye. $\varphi$ -contractibility and character contractibility of Fréchet algebras. Ann. Funct. Anal. 8 (2017), no. 1, 75--89. doi:10.1215/20088752-3764415.

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  • [1] F. Abtahi, S. Rahnama, and A. Rejali, Semisimple Segal Fréchet algebras, Period. Math. Hungar. 71 (2015), no. 2, 146–154.
  • [2] F. Abtahi, S. Rahnama, and A. Rejali, Weak amenability of Fréchet algebras, Politehn. Univ. Bucharest Sci. Bull. Ser. A. Appl. Math. Phys. 77 (2015), no. 4, 93–104.
  • [3] F. Abtahi, S. Rahnama, and A. Rejali, Segal Fréchet algebras, preprint, arXiv:1507.06577v1 [math.FA].
  • [4] M. Alaghmandan, R. Nasr-Isfahani, and M. Nemati, Character amenability and contractibility of abstract Segal algebras, Bull. Aust. Math. Soc. 82 (2010), no. 2, 274–281.
  • [5] J. T. Burnham, Closed ideals in subalgebras of Banach algebras, I, Proc. Amer. Math. Soc. 32 (1972), no. 2, 551–555.
  • [6] H. Goldmann, Uniform Fréchet Algebras, North-Holland Math. Stud. 162, North-Holland, Amsterdam, 1990.
  • [7] S. L. Gulick, The bidual of a locally multiplicatively-convex algebra, Pacific J. Math. 17 (1966), 71–96.
  • [8] A. Ya. Helemskii, The Homology of Banach and Topological Algebras, Math. Appl. 41, Kluwer, Dordrecht 1989.
  • [9] A. Ya. Helemskii, “31 problems of the homology of the algebras of analysis” in Linear and Complex Analysis: Problem Book 3, Part I, Lecture Notes in Math. 1573, Springer, New York, 1994, 54–78.
  • [10] A. Ya. Helemskii, “Homology for the algebras of analysis” in Handbook of Algebra, Vol. 2, North-Holland, Amsterdam, 2000, 151–274.
  • [11] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, II: Structure and Analysis for Compact Groups, 2nd ed., Grundlehren Math. Wiss. 152, Springer, New York, 1970.
  • [12] Z. Hu, M. S. Monfared, and T. Traynor, On character amenable Banach algebras, Studia Math. 193 (2009), no. 1, 53–78.
  • [13] P. Lawson and C. J. Read, Approximate amenability of Fréchet algebras, Math. Proc. Cambridge Philos. Soc. 145 (2008), no. 2, 403–418.
  • [14] R. Meise and D. Vogt, Introduction to Functional Analysis, Oxf. Grad. Texts Math. 2, Oxford Univ. Press, New York, 1997.
  • [15] A. Yu. Pirkovskii, Flat cyclic Fréchet modules, amenable Fréchet algebras, and approximate identities, Homology Homotopy Appl. 11 (2009), no. 1, 81–114.
  • [16] H. Reiter, $L^{1}$-Algebras and Segal Algebras, Lecture Notes in Math. 231, Springer, Berlin, 1971.
  • [17] H. H. Schaefer, Topological Vector Spaces, Grad. Texts in Math. 3, Springer, New York, 1971.
  • [18] L. B. Schweitzer, Dense nuclear Fréchet ideals in $C^{*}$-algebras, preprint, arXiv:1205.0089v10 [math.OA].
  • [19] M. Sugiura, Fourier series of smooth functions on compact Lie groups, Osaka, J. Math. 8 (1971), 33–47.
  • [20] J. L. Taylor, Homology and cohomology for topological algebras, Adv. Math. 9 (1972), 137–182.
  • [21] F. Trèves, Topological Vector Spaces, Distributions and Kernels, Dover, Mineola, NY, 2006.