# Norms related to binomial series

Hunziker, H; Jarchow, H (2010). Norms related to binomial series. In: Curbera, G P; Mockenhaupt, G; Ricker, W J. Vector measures, integration and related topics. Basel: Birkhäuser, 231-243.

## Abstract

We investigate norms related to the vectors h n =(h n (k)) k ∈ℕ in ℝℕ (or ℂℕ) (n∈ℕ) where
hn(k)=n!kk+1(k+n)=1kn+kn
We estimate, and in a few cases even calculate, the norms of the h n ’s as elements of the usual sequence spaces ℓ r . We also show that for ‘almost all’ p, q the matrix with entries h n (k) defines a bounded linear operator from ℓ p into ℓ q , with rather strong compactness properties.

## Abstract

We investigate norms related to the vectors h n =(h n (k)) k ∈ℕ in ℝℕ (or ℂℕ) (n∈ℕ) where
hn(k)=n!kk+1(k+n)=1kn+kn
We estimate, and in a few cases even calculate, the norms of the h n ’s as elements of the usual sequence spaces ℓ r . We also show that for ‘almost all’ p, q the matrix with entries h n (k) defines a bounded linear operator from ℓ p into ℓ q , with rather strong compactness properties.

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