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• W3082593019 abstract "In this paper, we study existence of isometric embedding of $S_q^m$ into $S_p^n$ where $1leq pneq qleq infty$ and $m,ngeq 2.$ We show that if there is a linear isometry from $S_q^m$ into $S_p^n$, where $(q,p)in(1,infty]times(1,infty)cup(1,2)times{infty}$ and $pneq q$ then we must have $q=2.$ This mostly generalizes a classical result of Lyubich and Vasserstein. Moreover, our work complements work of Junge, Xu, Parcet and others on isometric and almost isometric embedding theory on noncommutative $L_p$-spaces. Our methods rely on several new ingredients related to perturbation theory of linear operators, namely Kato-Rellich theorem, theory of multiple operator integrals and Birkhoff-James orthogonality, followed by thorough and careful case by case analysis. The case $1<q<2$ and $p=infty$ was left open in cite{Ra20}." @default.
• W3082593019 created "2020-09-08" @default.
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• W3082593019 date "2020-08-30" @default.
• W3082593019 modified "2023-09-23" @default.
• W3082593019 title "Isometric Embedding of $S_q^m$ into $S_p^n$" @default.
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