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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  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. 
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