Isometries between Schatten-$p$ classes

Abstract: Isometries between commutative and non-commutative $L_p$-spaces have a long history which starts from the seminal work of Banach himself. However, despite many remarkable results and characterization theorems not much is known when finite dimensional Schatten-$p$ classes embed between each other. In this direction, together with my collaborators, I have some rigidity results about the isometric embeddability of finite dimensional Schatten-$p$ class. For example, if $2 < p<\infty$ and $T:\ell_p^2\to B(\ell_2)$ is an isometry, then $T (e_1),T(e_2) \in B(\ell_2) K(\ell_2)$. We also have applications in the direction of operator spaces. Interestingly, our methods are completely new and use various concepts such as Birkhoff-James orthogonality, norm parallelism, multiple operator integral and Kato-Rellich theorem in the perturbation of a linear operator.

functional analysisgroup theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Groups, Operators, and Banach Algebras Webinar

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