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- W4381611601 abstract "The existence of isometric embedding of $S_q^m$ into $S_p^n$ , where $1leq pneq qleq infty$ and $m,ngeq 2$ , has been recently studied in [6]. In this article, we extend the study of isometric embeddability beyond the above-mentioned range of $p$ and $q$ . More precisely, we show that there is no isometric embedding of the commutative quasi-Banach space $ell _q^m(mathbb {R})$ into $ell _p^n(mathbb {R})$ , where $(q,p)in (0,infty )times (0,1)$ and $pneq q$ . As non-commutative quasi-Banach spaces, we show that there is no isometric embedding of $S_q^m$ into $S_p^n$ , where $(q,p)in (0,2)setminus {1}times (0,1)$ $cup , {1}times (0,1)setminus left {!frac {1}{n}:nin mathbb {N}right }$ $cup , {infty }times (0,1)setminus left {!frac {1}{n}:nin mathbb {N}right }$ and $pneq q$ . Moreover, in some restrictive cases, we also show that there is no isometric embedding of $S_q^m$ into $S_p^n$ , where $(q,p)in [2, infty )times (0,1)$ . A new tool in our paper is the non-commutative Clarkson's inequality for Schatten class operators. Other tools involved are the Kato–Rellich theorem and multiple operator integrals in perturbation theory, followed by intricate computations involving power-series analysis." @default.
- W4381611601 created "2023-06-23" @default.
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- W4381611601 date "2023-06-22" @default.
- W4381611601 modified "2023-10-16" @default.
- W4381611601 title "On isometric embeddability of into as non-commutative quasi-Banach spaces" @default.
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- W4381611601 doi "https://doi.org/10.1017/prm.2023.54" @default.
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