Nonlinear * -Lie higher derivations of standard operator algebras

Mohammad Ashraf; Shakir Ali; Bilal Ahmad Wani

Communications in Mathematics (2018)

  • Volume: 26, Issue: 1, page 15-29
  • ISSN: 1804-1388

Abstract

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Let ℋ be an infinite-dimensional complex Hilbert space and 𝔄  be a standard operator algebra on ℋ which is closed under the adjoint operation. It is shown that every nonlinear * -Lie higher derivation 𝒟 = { δ n } n ∈ ℕ of 𝔄 is automatically an additive higher derivation on 𝔄 . Moreover, 𝒟 = { δ n } n ∈ ℕ is an inner * -higher derivation.

How to cite

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Ashraf, Mohammad, Ali, Shakir, and Wani, Bilal Ahmad. "Nonlinear $\ast $-Lie higher derivations of standard operator algebras." Communications in Mathematics 26.1 (2018): 15-29. <http://eudml.org/doc/294361>.

@article{Ashraf2018,
abstract = {Let $\mathcal \{H\}$ be an infinite-dimensional complex Hilbert space and $\mathfrak \{A\}$ be a standard operator algebra on $\mathcal \{H\}$ which is closed under the adjoint operation. It is shown that every nonlinear $\ast $-Lie higher derivation $\mathcal \{D\}=\lbrace \{\delta _n\}\rbrace _\{n\in \mathbb \{N\}\}$ of $\mathfrak \{A\}$ is automatically an additive higher derivation on $\mathfrak \{A\}$. Moreover, $\mathcal \{D\}=\lbrace \{\delta _n\}\rbrace _\{n\in \mathbb \{N\}\}$ is an inner $\ast $-higher derivation.},
author = {Ashraf, Mohammad, Ali, Shakir, Wani, Bilal Ahmad},
journal = {Communications in Mathematics},
keywords = {Nonlinear $\ast $-Lie derivation; nonlinear $\ast $-Lie higher derivation; additive $\ast $-higher derivation; standard operator algebra},
language = {eng},
number = {1},
pages = {15-29},
publisher = {University of Ostrava},
title = {Nonlinear $\ast $-Lie higher derivations of standard operator algebras},
url = {http://eudml.org/doc/294361},
volume = {26},
year = {2018},
}

TY - JOUR
AU - Ashraf, Mohammad
AU - Ali, Shakir
AU - Wani, Bilal Ahmad
TI - Nonlinear $\ast $-Lie higher derivations of standard operator algebras
JO - Communications in Mathematics
PY - 2018
PB - University of Ostrava
VL - 26
IS - 1
SP - 15
EP - 29
AB - Let $\mathcal {H}$ be an infinite-dimensional complex Hilbert space and $\mathfrak {A}$ be a standard operator algebra on $\mathcal {H}$ which is closed under the adjoint operation. It is shown that every nonlinear $\ast $-Lie higher derivation $\mathcal {D}=\lbrace {\delta _n}\rbrace _{n\in \mathbb {N}}$ of $\mathfrak {A}$ is automatically an additive higher derivation on $\mathfrak {A}$. Moreover, $\mathcal {D}=\lbrace {\delta _n}\rbrace _{n\in \mathbb {N}}$ is an inner $\ast $-higher derivation.
LA - eng
KW - Nonlinear $\ast $-Lie derivation; nonlinear $\ast $-Lie higher derivation; additive $\ast $-higher derivation; standard operator algebra
UR - http://eudml.org/doc/294361
ER -

References

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