A note on zero Lie product determined nest algebras as Banach algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran.

2 Department of Mathematics, Payam Noor University of Technology, P.O. Box 19395-3697, Tehran, Iran.

10.22072/wala.2020.130358.1293

Abstract

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.

Keywords

References

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Wavelet and Linear Algebra
Volume 8, Issue 1
Spring- Summer
2021
Pages 1-6

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