A cb-Bohnenblust–Hille inequality with constant one and its applications in learning theory
Year: 2025
Type: article
Abstract: The main result of this work shows that Bohnenblust–Hille inequality for m-homogeneous polynomials holds with constant one when the infinity norm is replaced by the completely bounded norm. Moreover, we show that this inequality finds some interesting consequences in quantum learning theory. In the second part of this paper, we broaden our investigation of the Bohnenblust–Hille inequality to other contexts. In particular, we extend recent results by Volberg and Zhang, demonstrating its applicability within a framework we have termed “Learning Low-Degree Quantum Objects”.
Source: Mathematische Annalen
Authors: Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez, Carlos Palazuelos
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G1175115578, G1401168639, NETWORKS Doctoral Program, G1855990336, G1908868068, G2262748287, G2309174360, G24120701, G252646220, G2601397997, G2660406951, G294895050, G300979063, G3480869486, G3518538256, G3681454997, G4042783231, G4192779913, G425668148, G430777504, G434337789, G4364530112, G455862292, G464105488, G5080475149, G5195188938, G5421974903, G565383568, G6346387488, G638709848, G7084143925, G7780475403, G8575141037, G884803548, G99296377
OpenAlex ID: W4410108046