On Maps that Preserve the Lie Products Equal to Fixed Elements

Shiv Kumar Chaudhary; Om Prakash

paper

On Maps that Preserve the Lie Products Equal to Fixed Elements

arXiv:2512.24912

Abstract

This work characterizes the general form of a bijective linear map $I^¨ : M_{n} (C) \to M_{n} (C)$ such that $[I^¨ (A_{1}), I^¨ (A_{2})] = D_{2}$ whenever $[A_{1}, A_{2}] = D_{1}$ where $D_{1} and D_{2}$ are fixed matrices. Additionally, let $H_{1}$ and $H_{2}$ be the infinite-dimensional complex Hilbert spaces. We characterize the bijective linear map $I^¨ : B (H_{1}) \to B (H_{2})$ where $I^¨ (A_{1}) \circ I^¨ (A_{2}) = D_{2}$ whenever $A_{1} \circ A_{2} = D_{1}$ and $D_{1} and D_{2}$ are fixed operators.

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