ON THE NUMERICAL RANGE WITH RESPECT TO A FAMILY OF PROJECTIONS

Dada W., Kerner J., ERKURŞUN ÖZCAN N.

METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, vol.24, no.4, pp.297-304, 2018 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 4
  • Publication Date: 2018
  • Journal Name: METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.297-304
  • Hacettepe University Affiliated: Yes

Abstract

In this note we introduce the concept of a numerical range of a bounded linear operator on a Hilbert space with respect to a family of projections. We give a precise definition and elaborate on its connection to the classical numerical range as well as to generalizations thereof such as the quadratic numerical range, block numerical range, and product numerical range. In general, the importance of this new notion lies within its unifying aspect.