Hostname: page-component-54dcc4c588-mz6gc Total loading time: 0 Render date: 2025-09-12T10:15:36.801Z Has data issue: false hasContentIssue false
  • English
  • Français

WELL-BOUNDEDNESS OF SUMS AND PRODUCTS OF OPERATORS

Published online by Cambridge University Press:  08 August 2003

IAN DOUST  and
T. A. GILLESPIE
IAN DOUST
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australiai.doust@unsw.edu.au
T. A. GILLESPIE
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Edinburgh EH9 3JZ t.a.gillespie@edinburgh.ac.uk
Get access

Abstract

A sufficient condition is given under which the sum, product and indeed any polynomial combination of a well-bounded operator and a commuting real scalar-type spectral operator is well-bounded. This generalizes a result of Gillespie for Hilbert space operators. It is shown in particular that if $X$ is a UMD space, then the sum of finitely many commuting real scalar-type spectral operators acting on $X$ is a well-bounded operator (a result which fails on general reflexive Banach spaces).

Keywords

47B40

Information

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 183 - 192
Copyright
The London Mathematical Society 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable