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.
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.
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.
| Item Type: | Book Section, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Language: | English |
| Date: | 2010 |
| Deposited On: | 17 Feb 2012 21:13 |
| Last Modified: | 23 Jan 2022 20:51 |
| Publisher: | Birkhäuser |
| Series Name: | Operator Theory: Advances and Applications |
| Number: | 201 |
| ISSN: | 0255-0156 |
| ISBN: | 978-3-0346-0210-5 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1007/978-3-0346-0211-2_21 |
Hunziker, H