Strictly singular non-compact operators between spaces

  • Francisco L. Hernández

    Universidad Complutense de Madrid, Spain
  • Evgeny M. Semenov

    Voronezh State University, Russia
  • Pedro Tradacete

    Instituto de Ciencias Matemáticas (ICMAT), Madrid, Spain
Strictly singular non-compact operators between $L_p$ spaces cover
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Abstract

We study the structure of strictly singular non-compact operators between spaces. Answering a question raised in earlier work on interpolation properties of strictly singular operators, it is shown that there exist operators , for which the set of points such that is strictly singular but not compact contains a line segment in the triangle of any positive slope. This will be achieved by means of Riesz potential operators between metric measure spaces with different Hausdorff dimension. The relation between compactness and strict singularity of regular (i.e., difference of positive) operators defined on subspaces of is also explored.

Cite this article

Francisco L. Hernández, Evgeny M. Semenov, Pedro Tradacete, Strictly singular non-compact operators between spaces. Rev. Mat. Iberoam. 39 (2023), no. 1, pp. 181–200

DOI 10.4171/RMI/1360