2 research outputs found
On Isometric Embeddability of into as non-commutative Quasi-Banach spaces
The existence of isometric embedding of into , where and has been recently studied in \cite{JFA22}.
In this article, we extend the study of isometric embeddability beyond the
above mentioned range of and . More precisely, we show that there is no
isometric embedding of the commutative quasi-Banach space into
, where and . As
non-commutative quasi-Banach spaces, we show that there is no isometric
embedding of into , where and .
Moreover, in some restrictive cases, we also show that there is no isometric
embedding of into , where . To
achieve our goal we significantly use Kato-Rellich theorem and multiple
operator integrals in perturbation theory, followed by intricate computations
involving power-series analysis.Comment: 18 page