# Norms related to binomial series - Zurich Open Repository and Archive

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.

## Altmetrics

Item Type: Book Section, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2010 17 Feb 2012 21:13 05 Apr 2016 15:33 Birkhäuser Operator Theory: Advances and Applications 201 0255-0156 978-3-0346-0210-5 https://doi.org/10.1007/978-3-0346-0211-2_21