View More View Less
  • 1 University of Kurdistan, P. O. Box 416, Sanandaj, Iran
Full access


Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of operator algebras on the Hilbert C*-module X called operator algebras with property k and operator algebras with property ℤ, and we study the first (continuous) cohomology group of them with coefficients in various Banach bimodules under several conditions on B and X. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1]

    Brown, L. G., Stable isomorphism of hereditary subalgebras of C*-algebras, Pacific J. Math., 71 (1977), 335348.

  • [2]

    Chernoff, P. R., Representations, automorphisms, and derivations of some operator algebras, J. Funct. Anal., 12 (1973), 275289.

  • [3]

    Christensen, E., Derivations of nest algebras, Math. Ann., 229 (1977), 155161.

  • [4]

    He, J., Li, J. and Zhao, D., Derivations, local and 2-local derivations on some algebras of operators on Hilbert C*-modules, Mediterr. J. Math., 14 (230) (2017).

    • Search Google Scholar
    • Export Citation
  • [5]

    Johnson, B. E. and Sinclair, A. M., Continuity of derivations and a problem of Kaplansky, Am. J. Math., 90 (1968), 10671073.

  • [6]

    Kadison, R. V., Derivations of operator algebras, Ann. Math., 83 (2) (1966), 280293.

  • [7]

    Kaplansky, I., Modules over operator algebras, Amer. J. Math., 75 (1953), 839853.

  • [8]

    Lance, C., Hilbert C*-modules, London Math. Soc. Lecture Notes Series, 210, Cambridge University Press, Cambridge, 1995.

  • [9]

    Li, P., Han, D. and Tang, W., Derivations on the algebras of operators in Hilbert C*-modules, Acta Math. Sinca (Engl. Ser)., 28 (2012), 16151622.

    • Search Google Scholar
    • Export Citation
  • [10]

    Manuilov, V. M. and Troitsky, E. V., Hilbert C*-modules, Translation of Mathematical Monograph, 226, American Mathematical Society, Providence, RI, 2005.

    • Search Google Scholar
    • Export Citation
  • [11]

    Moghadam, M. K., Miri, M. and Janfada, A., A note on derivations on the algebra of operators in Hilbert C * -modules, Mediterr. J. Math., 13 (2016), 11671175.

    • Search Google Scholar
    • Export Citation
  • [12]

    Palmer, T. W., Banach algebras and the general theory of *-algebras, Volume, Algebras and Banach algebras, Cambridge University Press, Cambridge, 1994.

    • Search Google Scholar
    • Export Citation
  • [13]

    Paschke, W., Inner product modules over B*-algebra, Trans. Amer. Math. Soc., 182 (1973), 443468.

  • [14]

    Rieffel, M. A., Induced representations of C*-algebras, Adv. In Math., 13 (1974), 176257.

  • [15]

    Sahleh, A. and Najarpisheh, L., Derivations of operators on Hilbert modules, Gen. Math. Notes., 24 (1) (2014), 5257.

  • [16]

    Sakai, S., Derivations of W*-algebras, Ann. Math., 83 (1966), 273279.

  • [17]

    Sakai, S., Derivations of simple C*-algebras, J. Funct. Anal., 2 (1968), 202206.

  • [18]

    Sakai, S., Derivations of simple C*-algebras II, Bull. Soc. Math. France, 99 (1971), 259263.

  • [19]

    Thomas, M. P., The image of a derivation is contained in the radical, Ann. Math., 128 (1988), 435460.

  • Impact Factor (2018): 0.309
  • Mathematics (miscellaneous) SJR Quartile Score (2018): Q3/li>
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • The ISI Alerting Services


Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE