Factorizations for quasi-Banach time-frequency spaces and Schatten classes

2023/07/04 by Divyang G. Bhimani, Bhimani, Divyang, Joachim Toft +1
Mathematics · #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2307.01590

Abstract

We deduce factorization properties for a quasi-Banach module over a quasi-Banach algebra. Especially we extend a result by Hewitt and prove that if any such algebra which possess a bounded left approximate identity, then any element in the module can be factorized. As applications, we deduce factorization properties for Wiener amalgam spaces, for an extended family of modulation spaces and for Schatten symbol classes in pseudo-differential calculus under multiplications like convolutions, twisted convolutions and symbolic products. For example we show for Wiener amalgam spaces that WL^1,r*WL^p,q=WL^p,q when r in (0,1], and p and q are finite and larger than r. In particular we improve Rudin's identity L¹*L¹=L¹.

Related

• Wiener Amalgam Spaces with respect to Quasi-Banach Spaces
• On algebras which are inductive limits of Banach spaces
• Further study of modulation spaces as Banach algebras
• Symmetrization, factorization and arithmetic of quasi-Banach function spaces
• Factorisation in stopping-time Banach spaces: identifying unique maximal ideals