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Tensor products of regularly varying sequences
Author(s) -
Pietsch Albrecht
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700083
Subject(s) - tensor product of hilbert spaces , tensor product , mathematics , tensor (intrinsic definition) , hilbert space , pure mathematics , space (punctuation) , tensor contraction , product (mathematics) , symmetric tensor , stability (learning theory) , tensor product of algebras , cartesian tensor , algebra over a field , tensor density , mathematical analysis , tensor field , geometry , exact solutions in general relativity , linguistics , computer science , philosophy , machine learning
We investigate how asymptotic properties of real sequences s = ( σ m ) and t = ( τ n ) are passed on to their tensor product s ⊗ t = ( σ m τ n ) . The main result concerns sequences of the formx γ ϱ : = (( 1 + log 2 ℓ ) γ ℓ ϱ)with ℓ = 1 , 2 , ⋯ , ϱ > 0 ,andγ ∈ R .This problem is closely related to tensor stability of operator ideals on the Hilbert space.