On Componental Operators in Hilbert Space

Andrzej Cegielski, Yair Censor

Research output: Contribution to journalArticlepeer-review


We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by “componental operators” acting on the Hilbert spaces that form the product space. We attribute operatorial properties to the componental operators rather than to the full operators. The operatorial properties that we discuss include nonexpansivity, firm nonexpansivity, relaxed firm nonexpansivity, averagedness, being a cutter, quasi-nonexpansivity, strong quasi-nonexpansivity, strict quasi-nonexpansivity and contraction. Some relationships between operators whose componental operators have such properties and operators that have these properties on the product space are studied. This enables also to define componental fixed point sets and to study their properties. For componental contractions we offer a variant of the Banach fixed point theorem. Our motivation comes from the desire to extend a fully-simultaneous method that takes into account sparsity of the linear system in order to accelerate convergence. This was originally applicable to the linear case only and gives rise to an iterative process that uses different componental operators during iterations.

Original languageEnglish
Pages (from-to)1555-1571
Number of pages17
JournalNumerical Functional Analysis and Optimization
Issue number13
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.


  • Componental operators
  • Hilbert spaces
  • fixed point
  • nonexpansive operator
  • quasi-nonexpansive operator

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization


Dive into the research topics of 'On Componental Operators in Hilbert Space'. Together they form a unique fingerprint.

Cite this