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Transactions of the American Mathematical Society

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On derivations of certain algebras related to irreducible triangular algebras

Author: Baruch Solel
Journal: Trans. Amer. Math. Soc. 277 (1983), 263-273
MSC: Primary 46L55; Secondary 47D99
MathSciNet review: 690051
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Abstract: This paper deals with derivations on algebras that are generated by a maximal abelian selfadjoint algebra of operators $ \mathcal{A}$ on a Hilbert space and a group of unitary operators acting on it. A necessary and sufficient condition for such a derivation to be implemented by an operator affiliated with $ \mathcal{A}$ is given. The results are related to the study of derivations on a certain class of irreducible triangular algebras.

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  • [1] William Arveson, On groups of automorphisms of operator algebras, J. Functional Analysis 15 (1974), 217–243. MR 0348518
  • [2] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
  • [3] Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
  • [4] Richard V. Kadison and I. M. Singer, Triangular operator algebras. Fundamentals and hyperreducible theory., Amer. J. Math. 82 (1960), 227–259. MR 0121675,
  • [5] Gert K. Pedersen, 𝐶*-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
  • [6] J. R. Ringrose, Cohomology of operator algebras, Lectures on operator algebras (Tulane Univ. Ring and Operator Theory Year, 1970–1971, Vol. II; dedicated to the memory of David M. Topping), Springer, Berlin, 1972, pp. 355–434. Lecture Notes in Math., Vol. 247. MR 0383102
  • [7] Shôichirô Sakai, 𝐶*-algebras and 𝑊*-algebras, Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60. MR 0442701
  • [8] B. Solel, Irreducible triangular algebras, Thesis, Univ. of Pennsylvania, 1981.

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Article copyright: © Copyright 1983 American Mathematical Society