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Bibliographic Details
Main Author: Plakhotnikov, Alexander
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.24135
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author Plakhotnikov, Alexander
author_facet Plakhotnikov, Alexander
contents This work investigates continuous embeddings for quantum Sobolev spaces $\mathfrak{H}_γ^{s,p}(G,H)$ into Schatten--von Neumann classes $S_r(H)$. We try to extend the results of Lakmon and Mensah to the case where the operators belong to Schatten classes $S_p(H)$ for $p \neq 2$. We establish that these quantum Sobolev spaces are Banach spaces and, by employing a duality argument, we define spaces for $p>2$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_24135
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On continuous embeddings of quantum Sobolev spaces into Schatten classes $\mathfrak{H}_γ^{s,p}(G,H) \hookrightarrow S_p(H)$
Plakhotnikov, Alexander
Functional Analysis
47B90, 43A25, 47A62
This work investigates continuous embeddings for quantum Sobolev spaces $\mathfrak{H}_γ^{s,p}(G,H)$ into Schatten--von Neumann classes $S_r(H)$. We try to extend the results of Lakmon and Mensah to the case where the operators belong to Schatten classes $S_p(H)$ for $p \neq 2$. We establish that these quantum Sobolev spaces are Banach spaces and, by employing a duality argument, we define spaces for $p>2$.
title On continuous embeddings of quantum Sobolev spaces into Schatten classes $\mathfrak{H}_γ^{s,p}(G,H) \hookrightarrow S_p(H)$
topic Functional Analysis
47B90, 43A25, 47A62
url https://arxiv.org/abs/2509.24135