TY - JOUR
ID - 245222
TI - A note on zero Lie product determined nest algebras as Banach algebras
JO - Wavelet and Linear Algebra
JA - WALA
LA - en
SN - 2383-1936
AU - Ghahramani, Hoger
AU - Fallahi, Kamal
AU - Khodakarami, Wania
AD - Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran.
AD - Department of Mathematics, Payam Noor University of Technology, P.O. Box 19395-3697, Tehran, Iran.
Y1 - 2021
PY - 2021
VL - 8
IS - 1
SP - 1
EP - 6
KW - Zero Lie product determined Banach algebra
KW - nest algebra
KW - weakly amenable Banach algebra
DO - 10.22072/wala.2020.130358.1293
N2 - A Banach algebra $\A$ is said to be zero Lie product determined Banach algebra if for every continuous bilinear functional $\phi:\A \times \A\rightarrow \mathbb{C}$ the following holds: if $\phi(a,b)=0$ whenever $ab=ba$, then there exists some $\tau \in \A^*$ such that $\phi(a,b)=\tau(ab-ba)$ for all $a,b\in \A$. We show that any finite nest algebra over a complex Hilbert space is a zero Lie product determined Banach algebra.
UR - http://wala.vru.ac.ir/article_245222.html
L1 - http://wala.vru.ac.ir/article_245222_bba88ea53ec7d84e8f04748e3bd83bb6.pdf
ER -