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1993 | 105 | 1 | 77-92
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Interpolation by elementary operators

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EN
Given two n-tuples $a = (a_1,...,a_n)$ and $b = (b_1,...,b_n)$ of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that $Ea_j = b_j$ for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in $A^n$.
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Twórcy
  • Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 61000, Slovenia
Bibliografia
  • [1] C. Apostol and L. Fialkow, Structural properties of elementary operators, Canad. J. Math. 38 (1986), 1485-1524.
  • [2] K. R. Davidson, Nest Algebras, Pitman Res. Notes in Math. 191, Pitman, 1988.
  • [3] L. Fialkow, The range inclusion problem for elementary operators, Michigan Math. J. 34 (1987), 451-459.
  • [4] I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Transl. Math. Monographs 18, Amer. Math. Soc., Providence, R.I., 1969.
  • [5] B. E. Johnson, Centralizers and operators reduced by maximal ideals, J. London Math. Soc. 43 (1968), 231-233.
  • [6] R. V. Kadison, Local derivations, J. Algebra 130 (1990), 494-509.
  • [7] R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, Vols. I and II, Academic Press, London 1983 and 1986.
  • [8] D. R. Larson and A. R. Sourour, Local derivations and local automorphisms of B(X), in: Proc. Sympos. Pure Math. 51, Part 2, Amer. Math. Soc., 1990, 187-194.
  • [9] B. Magajna, A system of operator equations, Canad. Math. Bull. 30 (1987), 200-209.
  • [10] B. Magajna, A transitivity theorem for algebras of elementary operators, Proc. Amer. Math. Soc., to appear.
  • [11] M. Mathieu, Elementary operators on prime C*-algebras I, Math. Ann. 284 (1989), 223-244.
  • [12] M. Mathieu, Rings of quotients of ultraprime Banach algebras, with applications to elementary operators, Proc. Centre Math. Anal. Austral. Nat. Univ. 21 (1989), 297-317.
  • [13] G. K. Pedersen, Analysis Now, Graduate Texts in Math. 118, Springer, New York 1989.
  • [14] V. S. Šulman, Operator algebras with strongly cyclic vectors, Mat. Zametki 16 (1974), 253-257 (in Russian).
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv105i1p77bwm
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