Opuscula Math. 36, no. 6 (2016), 787-797

Opuscula Mathematica

Elementary operators - still not elementary?

Martin Mathieu

Abstract. Properties of elementary operators, that is, finite sums of two-sided multiplications on a Banach algebra, have been studied under a vast variety of aspects by numerous authors. In this paper we review recent advances in a new direction that seems not to have been explored before: the question when an elementary operator is spectrally bounded or spectrally isometric. As with other investigations, a number of subtleties occur which show that elementary operators are still not elementary to handle.

Keywords: spectral isometries, elementary operators, Jordan isomorphisms.

Mathematics Subject Classification: 47B47, 46H99, 47A10, 47A65, 47B48.

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  • Martin Mathieu
  • Queen's University Belfast, Pure Mathematics Research Centre, Belfast BT7 1NN, Northern Ireland
  • Communicated by P.A. Cojuhari.
  • Received: 2016-04-17.
  • Accepted: 2016-07-28.
  • Published online: 2016-10-29.
Opuscula Mathematica - cover

Cite this article as:
Martin Mathieu, Elementary operators - still not elementary?, Opuscula Math. 36, no. 6 (2016), 787-797, http://dx.doi.org/10.7494/OpMath.2016.36.6.787

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