2017/04/14 by Elif Uyanık, Uyanık, Elif, Murat Yurdakul +2
Mathematics · #46A03 #46A04 #46A32 #46A45 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46A03 #msc:46A04 #msc:46A32 #msc:46A45
paper · pdf · doi:10.48550/arxiv.1704.04395
9 pages
arxiv created 2017/04/14 · openalex publication_date 2017/04/14 · arxiv updated 2017/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For Fréchet spaces E and F we write (E,F) ∈ B if every continuous linear operator from E to F is bounded. Let l be a Banach sequence space with a monotone norm in which the canonical system (en) is an unconditional basis. We obtain a necessary and sufficient condition for (E,F) ∈ B when F = λl(B). We say that a triple (E,F,G) has the bounded factorization property and write (E,F,G) ∈ BF if each continuous linear operator T : E \longrightarrow G that factors over F is bounded. We extend some results in \citeTer03 to l-Köthe spaces and obtain a sufficient condition for (E,λl1(A) otimespi λl2(B), λl3(C)) ∈ BF when λl1(A) and λl2(B) are nuclear.