Interpolation by elementary operators

Studia Mathematica (1993)

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

top

Abstract

top
Given two n-tuples $a=\left({a}_{1},...,{a}_{n}\right)$ and $b=\left({b}_{1},...,{b}_{n}\right)$ 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

top

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

top
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).

NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.