English

Numerical radius norm and extreme contractions of $L(H)$

Functional Analysis 2022-10-19 v1

Abstract

Suppose L(H)L(H) is the space of all bounded linear operators on a complex Hilbert space H.H. This article deals with the problem of characterizing the extreme contractions of L(H)L(H) with respect to the numerical radius norm on L(H).L(H). In contrast to the usual operator norm, it is proved that there exists a class of unitary operators on HH which are not extreme contractions when the numerical radius norm is considered on L(H).L(H). Moreover, there are non-unitary operators on HH which are extreme contractions as far as the numerical radius norm is concerned.

Keywords

Cite

@article{arxiv.2210.09734,
  title  = {Numerical radius norm and extreme contractions of $L(H)$},
  author = {Arpita Mal},
  journal= {arXiv preprint arXiv:2210.09734},
  year   = {2022}
}