A Pełczyński-Vogt decomposition result for (PLS)-spaces and sequence space representations

2025/11/28 by Andreas Debrouwere, Debrouwere, Andreas, Lenny Neyt +1
Mathematics · #Mathematical Analysis and Transform Methods #Holomorphic and Operator Theory #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2511.23130

Abstract

We establish a Pelczyński-Vogt decomposition result for (PLS)-type power series spaces of infinite type. By combining this result with the theory of Gabor frames, we obtain sequence space representations for multiplier spaces of Gelfand-Shilov spaces of Beurling type.

Citations

• Sequence space representations of Beurling-Björck spaces via Gabor frames and Wilson bases
• A note on the barrelledness of weighted (PLB)-spaces of ultradifferentiable functions
• Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators
• Weighted (PLB)-spaces of ultradifferentiable functions and multiplier spaces
• Inclusion theorems for the Moyal multiplier algebras of generalized\n Gelfand-Shilov spaces
• Sequence space representations for spaces of entire functions with rapid decay on strips
• Anisotropic Shubin operators and eigenfunctions expansions in Gelfand-Shilov spaces
• Produits tensoriels topologiques et espaces nucléaires

Related

• Sequence space representations of Beurling-Björck spaces via Gabor frames and Wilson bases
• Sequence space representations for spaces of entire functions with rapid decay on strips
• p_Hahn Sequence Space
• Kadec-Pelczynski decomposition for Haagerup L_p-spaces
• On the inclusion relations between Gelfand-Shilov spaces