2014/06/29 by Said Amana Abdillah, Abdillah, Said Amana, Jean Esterle +5
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA
paper · pdf · doi:10.48550/arxiv.1406.7546
18 pages, in French
arxiv created 2014/06/29 · openalex publication_date 2014/06/29 · arxiv updated 2014/07/01 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operators: p-summing operators, γ-summing or γ-radonifying operators, weakly *1-nuclear operators and classes of operators defined via factorization properties. We introduce the class PS2(E; F) of pre-Hilbert-Schmidt operators as the class of all operators u:E→ F such that w∘ u ∘ v is Hilbert-Schmidt for every bounded operator v: H1→ E and every bounded operator w:F→ H2, where H1 et H2 are Hilbert spaces. Besides the trivial case where one of the spaces E or F is a "Hilbert-Schmidt space", this space seems to have been described only in the easy situation where one of the spaces E or F is a Hilbert space.