Approximation numbers of weighted composition operators - Archive ouverte HAL Access content directly
Other Publications Year : 2016

## Approximation numbers of weighted composition operators

, (1) , (2) , (3)
1
2
3
Gandalf Lechner,
• Function : Author
• PersonId : 995432
Daniel Li
Hervé Queffélec
• Function : Author
Luis Rodríguez-Piazza
• Function : Author

#### Abstract

We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circ\varphi)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight $w$ can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples).

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-01410297 , version 1 (06-12-2016)

### Identifiers

• HAL Id : hal-01410297 , version 1
• ARXIV :

### Cite

Gandalf Lechner,, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. Approximation numbers of weighted composition operators . 2016. ⟨hal-01410297⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

78 View