Skip to main content Accessibility help
×
Home

POSITIVE DEFINITE FUNCTIONS AND SEBESTYÉN'S OPERATOR MOMENT PROBLEM

  • ZOLTÁN SEBESTYÉN (a1) and DAN POPOVICI (a2)

Abstract

Given a sequence $\{A_n\}_{n\in\mathbb{Z}_+}$ of bounded linear operators between complex Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$ we characterize the existence of a contraction (resp. isometry, unitary operator, shift) $T$ on $\mathcal{K}$ such that \[A_n=T^nA_0,\quad n\in\mathbb{Z}_+.\] Such moment problems are motivated by their connection with the dilatability of positive operator measures having applications in the theory of stochastic processes.

The solutions, based on the fact that a certain operator function attached to $T$ is positive definite on $\mathbb{Z}$, extend the ones given by Sebestyén in [18], [19] or, recently, by Jabłoński and Stochel in [8]. Some applications, containing new characterizations for isometric, unitary operators, orthogonal projections or commuting pairs having regular dilation, conclude the paper.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      POSITIVE DEFINITE FUNCTIONS AND SEBESTYÉN'S OPERATOR MOMENT PROBLEM
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      POSITIVE DEFINITE FUNCTIONS AND SEBESTYÉN'S OPERATOR MOMENT PROBLEM
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      POSITIVE DEFINITE FUNCTIONS AND SEBESTYÉN'S OPERATOR MOMENT PROBLEM
      Available formats
      ×

Copyright

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed