More elementary operators that are spectrally bounded

Nadia Boudi; Martin Mathieu

More elementary operators that are spectrally bounded

Functional Analysis 2013-12-23 v1

Authors: Nadia Boudi , Martin Mathieu

Abstract

We discuss some necessary and some sufficient conditions for an elementary operator $x\mapsto\sum_{i=1}^n a_ixb_i$ on a Banach algebra $A$ to be spectrally bounded. In the case of length three, we obtain a complete characterisation when $A$ acts irreducibly on a Banach space of dimension greater than three.

Keywords

operator theory on banach spaces numerical range banach space

Cite

@article{arxiv.1312.6023,
  title  = {More elementary operators that are spectrally bounded},
  author = {Nadia Boudi and Martin Mathieu},
  journal= {arXiv preprint arXiv:1312.6023},
  year   = {2013}
}

Comments

23 pages

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