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Tensor products of regularly varying sequences

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  • Albrecht Pietsch

Abstract

We investigate how asymptotic properties of real sequences s=(σm) and t=(τn) are passed on to their tensor product s⊗t=(σmτn). The main result concerns sequences of the form xγϱ:=((1+log2ℓ)γℓϱ)withℓ=1,2,⋯,ϱ>0,andγ∈R.This problem is closely related to tensor stability of operator ideals on the Hilbert space.

Suggested Citation

  • Albrecht Pietsch, 2018. "Tensor products of regularly varying sequences," Mathematische Nachrichten, Wiley Blackwell, vol. 291(1), pages 109-127, January.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:1:p:109-127
    DOI: 10.1002/mana.201700083
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