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.

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.

## Citations

## Altmetrics

## Additional indexing

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: | 05 Apr 2016 15:33 |

Publisher: | Birkhäuser |

Series Name: | Operator Theory: Advances and Applications |

Number: | 201 |

ISSN: | 0255-0156 |

ISBN: | 978-3-0346-0210-5 |

Publisher DOI: | https://doi.org/10.1007/978-3-0346-0211-2_21 |

## Download

Full text not available from this repository.View at publisher

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.

You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.