On the connection between real and complex interpolation of quasi-Banach spaces
type: Item
instance of: scholarly article
title: On the connection between real and complex interpolation of quasi-Banach spaces
zbMATH Open document ID: 0953.46037
DOI: 10.1016/S0007-4497(98)80075-4
author: Fernando Cobos
author: Jaak Peetre
author: Lars-Erik Persson
published in: Bulletin des Sciences Mathématiques
publication date: 2000-09-28T00:00:00Z
review text: The authors generalize the formula (which is known for Banach couples) \[ [(A_0,A_1)_{\theta_0,q_0}, (A_0,A_1)_{\theta_1,q_1}]_\lambda= (A_0,A_1) _{\theta,q} \] to the case of quasi--Banach couples \((A_0,A_1)\). There are some earlier results to this question and the authors introduce a new approach to handle such spaces which works also in end--point cases. This gives (Theorem 5) the mapping of the right space to the left one above for \(0<\theta_0,\theta_1,\lambda<1,\;0<q_0,q_1<\infty\) or \(0<q_0<\infty\) and \(q_1=\infty\) (putting \(\theta=(1-\lambda)\theta_0+\lambda \theta_1,\;\frac {1} {q}=\frac {1-\lambda} {q_0}+\frac {\lambda} {q_1}\)). The other direction (Theorem 3) needs some technical condition on the couple \((A_0,A_1)\). Theorems 6 and 4 give corresponding results for end--point cases. Applications are given to function spaces and Schatten classes.
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 46A16
Mathematics Subject Classification ID: 46B70
zbMATH DE Number: 1138709
zbMATH Keywords: Banach couples
zbMATH Keywords: quasi-Banach spaces
zbMATH Keywords: function spaces
zbMATH Keywords: Schatten classes
zbMATH Keywords: complex interpolation
reviewed by: V. Losert
MaRDI profile type: Publication
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full work available at URL: s0007-4497(98)80075-4
OpenAlex ID: W2019916929
Wikidata QID: Q127861672
description: scientific article; zbMATH DE number 1138709