Skip to main content

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 19))

  • 2326 Accesses

Abstract

Suppose that A is an operator on a Hilbert space H. If λ does not belong to the spectrum of A, then the operator A - λ is invertible; write ρ(λ) = (A - λ)-1. (When it is necessary to indicate the dependence of the function p on the operator A, write ρ = ρ A .) The function ρ is called the resolvent of A. The domain of ρ is the complement of the spectrum of A; its values are operators on H.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1974 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Halmos, P.R. (1974). Spectral radius. In: A Hilbert Space Problem Book. Graduate Texts in Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-9976-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-9976-0_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4615-9978-4

  • Online ISBN: 978-1-4615-9976-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics