AI 中文总结
本研究证明Bourgain-Rosenthal-Schechtman空间具有SHAI性质，解决了Johnson等人2022年提出的相关问题。
AI 中文摘要
若Banach空间X满足：对任意非零Banach空间Y，从X上有界线性算子代数ℒ(X)到Y上有界线性算子代数ℒ(Y)的每个满射代数同态都是单射，则称X具有SHAI性质。本工作证明Bourgain-Rosenthal-Schechtman空间具有SHAI性质，从而回答了Johnson、Phillips与Schechtman在2022年提出的问题。
英文摘要
A Banach space $X$ has the SHAI property if, for every non-zero Banach space $Y$, every surjective algebra homomorphism from the algebra $\mathcal{L}(X)$ of bounded linear operators on $X$ onto $\mathcal{L}(Y)$ is injective. In this work, we prove that the Bourgain-Rosenthal-Schechtman spaces have the SHAI property, thereby answering a question posed by Johnson, Phillips, and Schechtman in 2022.
Comments17 pages
