Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 51 min ago
PreprintarXiv licencearXiv

Norms of generalized derivations with values in symmetric spaces

  • J. Huang
  • M. Pliev
  • F. Sukochev
  • R. Xu
Open at sourcePDFDOICite

Abstract

Let B(ℋ) be the *-algebra of all bounded linear operators on a Hilbert space ℋ. A classical result due to Stamplfi shows that, for any a∈ B(ℋ), the norm of the inner derivation δa=[a,·] on B(ℋ) is given by |δa|B(ℋ)→ B(ℋ)=2inf{ |a−cbf 1|B(ℋ):c∈ ℂ}. In the present paper, we provide a formula for the norm of a generalized derivation implemented by self-adjoint operators from an ideal in B(ℋ), which partially answers a question posed by Fialkow and Loebl in the 1980s. We also consider this question in a more general setting of a symmetrically normed (not necessarily complete or separable) space affiliated with a properly infinite semifinite von Neumann algebra.

Versions

Related

  1. Characterization of the Boundedness of a Generalized Fractional Maximal Operator in Weighted Lorentz Spaces for Certain Parameter Values
    Azhar Abek, Amiran Gogatishvili, Nurzhan Bokayev
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref
  2. A characterization of generalized derivations and biderivations on some simple algebras
    Hassan Oubba
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  3. On Rotationally Symmetric Norms
    Yossi Lonke
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Commutativity Criteria and Structural Properties of Prime Near-Rings Admitting Right Generalized Derivations on Specific Ideals
    Khaled Aldwoah, Inzamam ul Huque, Hafedh Alnoghashi +3
    AxiomsPeer-reviewedCC BY 4.0Algebra & number theoryCrossref
  5. Diagonalizable modular derivations on bigraded Poisson spaces and Koszul duality
    Ruobing Chen, Di Zhang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{huang2026norms,
  title = {{Norms of generalized derivations with values in symmetric spaces}},
  author = {J. Huang and M. Pliev and F. Sukochev and R. Xu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15233},
  eprint = {2609.15233},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15233},
}
RIS
TY  - UNPB
TI  - Norms of generalized derivations with values in symmetric spaces
AU  - J. Huang
AU  - M. Pliev
AU  - F. Sukochev
AU  - R. Xu
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15233
UR  - https://arxiv.org/abs/2609.15233
AB  - Let B(ℋ) be the *-algebra of all bounded linear operators on a Hilbert space ℋ. A classical result due to Stamplfi shows that, for any a∈ B(ℋ), the norm of the inner derivation δ_a=[a,·] on B(ℋ) is given by |δ_a|_B(ℋ)→ B(ℋ)=2inf{ |a−cbf 1|_B(ℋ):c∈ ℂ}. In the present paper, we provide a formula for the norm of a generalized derivation implemented by self-adjoint operators from an ideal in B(ℋ), which partially answers a question posed by Fialkow and Loebl in the 1980s. We also consider this question in a more general setting of a symmetrically normed (not necessarily complete or separable) space affiliated with a properly infinite semifinite von Neumann algebra.
ER  -