Elementary operators - still not elementary?
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.