# Infinite-dimensional triangularizable algebras

@article{Mesyan2018InfinitedimensionalTA,
title={Infinite-dimensional triangularizable algebras},
author={Zachary Mesyan},
journal={Forum Mathematicum},
year={2018},
volume={31},
pages={19 - 33}
}
• Zachary Mesyan
• Published 2018
• Mathematics
• Forum Mathematicum
• Abstract Let End k ⁢ ( V ) {\mathrm{End}_{k}(V)} denote the ring of all linear transformations of an arbitrary k-vector space V over a field k. We define X ⊆ End k ⁢ ( V ) {X\subseteq\mathrm{End}_{k}(V)} to be triangularizable if V has a well-ordered basis such that X sends each vector in that basis to the subspace spanned by basis vectors no greater than it. We then show that an arbitrary subset of End k ⁢ ( V ) {\mathrm{End}_{k}(V)} is strictly triangularizable (defined in the obvious way) if… CONTINUE READING

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