Skip to main content

On Operators Induced by General Finite-Rank Orthogonal Projections

  • 1017 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1992)

Abstract

In this chapter we further prepare the ground for the eigenvalue localization of elliptic global systems. Namely, in the following chapters we shall have to control the sandwitch (I –Π)B(I –Π) of an operator B, semi-bounded from below, by the orthogonal projectors (I –Π) relative to another operator A, semi-bounded from below. We present things in an abstract setting, for this is a useful machinery. Throughout this chapter H will always stand for a separable (infinite-dimensional) Hilbert space endowed with the scalar product (・, ・) = (・, ・)H.

Keywords

  • Compact Operator
  • Discrete Spectrum
  • Bounded Linear Operator
  • Hermitian Matrix
  • Resolvent Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alberto Parmeggiani .

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer Berlin Heidelberg

About this chapter

Cite this chapter

Parmeggiani, A. (2010). On Operators Induced by General Finite-Rank Orthogonal Projections. In: Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction. Lecture Notes in Mathematics(), vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11922-4_10

Download citation