2025/11/10 by Danko R. Jocić, Mihailo Krstić, Jocić, Danko R. +5
Mathematics · #47B47 (Primary) 47B49 47A30 47B10 (Secondary) #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2511.07613
openalex publication_date 2025/11/10 · openalex created_date 2025/11/13 · openalex updated_date 2026/07/28
Let q, r, s \geqslant 1 satisfy (1)/(2q) + (1)/(2r) = (1)/(s) and X ∈ Cs(H). If (λn)n=1∞, (wn)n=1∞ are sequences in (0,+∞) and (λn(1-q)/(2q) An)n=1∞, (λn1/(2q) An^*)n=1∞, (wn-1/(2r) Bn)n=1∞ and (wn(r-1)/(2r) Bn^*)n=1∞ are strongly square summable, then there exists \sideset^_\scriptstyle C\large s \phantom\textstyle∑n=1+∞AnXBn and \beginsplit amp;‖ \sideset^_\scriptscriptstyle \LargeC s \phantom ∑ n=1 ∞AnXBn‖s
amp;\leqslant‖ \sideset^_\scriptstyle s \phantom∑ n=1 ∞ λn(1)/(q) An An^* ‖ (1)/(2) - (1)/(2q) ‖ \sideset^_\scriptstyle s \phantom∑ n=1 ∞wn -(1)/(r) Bn^* Bn ‖ (1)/(2) - (1)/(2r) ‖ ( \sideset^_\scriptstyle s \phantom∑ n=1 ∞ λn (1)/(q)-1 An^* An ) (1)/(2q) X( \sideset^_\scriptstyle s \phantom∑ n=1 ∞ wn1-(1)/(r) Bn Bn^* ) (1)/(2r) ‖s . \endsplit Equivalent inequalities are also given, together with some applications to families (An)n=1∞ and (Bn)n=1∞ in B(H) which are not double square summable. The results presented in this article significantly extends the previous results of authors related to σ-elementary transformers in Schatten-von Neumann ideals.