Interpolation by elementary operators

Bojan Magajna

Studia Mathematica (1993)

  • Volume: 105, Issue: 1, page 77-92
  • ISSN: 0039-3223

Abstract

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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 E a 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 .

How to cite

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Magajna, Bojan. "Interpolation by elementary operators." Studia Mathematica 105.1 (1993): 77-92. <http://eudml.org/doc/215985>.

@article{Magajna1993,
abstract = {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 $A^n$.},
author = {Magajna, Bojan},
journal = {Studia Mathematica},
keywords = {elementary operators; C*-algebras; multipliers; interpolation by elementary operators; elementary operator; left multiplications; -algebra},
language = {eng},
number = {1},
pages = {77-92},
title = {Interpolation by elementary operators},
url = {http://eudml.org/doc/215985},
volume = {105},
year = {1993},
}

TY - JOUR
AU - Magajna, Bojan
TI - Interpolation by elementary operators
JO - Studia Mathematica
PY - 1993
VL - 105
IS - 1
SP - 77
EP - 92
AB - 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 $A^n$.
LA - eng
KW - elementary operators; C*-algebras; multipliers; interpolation by elementary operators; elementary operator; left multiplications; -algebra
UR - http://eudml.org/doc/215985
ER -

References

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  1. [1] C. Apostol and L. Fialkow, Structural properties of elementary operators, Canad. J. Math. 38 (1986), 1485-1524. Zbl0627.47015
  2. [2] K. R. Davidson, Nest Algebras, Pitman Res. Notes in Math. 191, Pitman, 1988. 
  3. [3] L. Fialkow, The range inclusion problem for elementary operators, Michigan Math. J. 34 (1987), 451-459. Zbl0644.47037
  4. [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. Zbl0181.13504
  5. [5] B. E. Johnson, Centralizers and operators reduced by maximal ideals, J. London Math. Soc. 43 (1968), 231-233. Zbl0157.20601
  6. [6] R. V. Kadison, Local derivations, J. Algebra 130 (1990), 494-509. Zbl0751.46041
  7. [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. Zbl0518.46046
  8. [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. Zbl0713.47045
  9. [9] B. Magajna, A system of operator equations, Canad. Math. Bull. 30 (1987), 200-209. 
  10. [10] B. Magajna, A transitivity theorem for algebras of elementary operators, Proc. Amer. Math. Soc., to appear. Zbl0799.46068
  11. [11] M. Mathieu, Elementary operators on prime C*-algebras I, Math. Ann. 284 (1989), 223-244. Zbl0648.46052
  12. [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. [13] G. K. Pedersen, Analysis Now, Graduate Texts in Math. 118, Springer, New York 1989. 
  14. [14] V. S. Šulman, Operator algebras with strongly cyclic vectors, Mat. Zametki 16 (1974), 253-257 (in Russian). 

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