Skip to main content Accessibility help
×
×
Home

ALMOST INVARIANT HALF-SPACES FOR OPERATORS ON HILBERT SPACE

  • IL BONG JUNG (a1), EUNGIL KO (a2) and CARL PEARCY (a3)

Abstract

The theory of almost invariant half-spaces for operators on Banach spaces was begun recently and is now under active development. Much less attention has been given to almost invariant half-spaces for operators on Hilbert space, where some techniques and results are available that are not present in the more general context of Banach spaces. In this note, we begin such a study. Our much simpler and shorter proofs of the main theorems have important consequences for the matricial structure of arbitrary operators on Hilbert space.

Copyright

Corresponding author

Footnotes

Hide All

The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1A2A2A01006072); the second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).

Footnotes

References

Hide All
[1] Androulakis, G., Popov, A., Tcaciuc, A. and Troitsky, V., ‘Almost invariant half-spaces of operators on Banach spaces’, Integral Equations Operator Theory 65 (2009), 473484.
[2] Bernik, J. and Radjavi, H., ‘Invariant and almost-invariant subspaces for pairs of idempotents’, Integral Equations Operator Theory 84 (2016), 283288.
[3] Marcoux, L., Popov, A. and Radjavi, H., ‘On almost-invariant subspaces and approximate commutation’, J. Funct. Anal. 264 (2013), 10881111.
[4] Popov, A., ‘Almost invariant half-spaces of algebras of operators’, Integral Equations Operator Theory 67 (2010), 247256.
[5] Popov, A. and Tcaciuc, A., ‘Every operator has almost-invariant subspaces’, J. Funct. Anal. 265 (2013), 257265.
[6] Sirotkin, G. and Wallis, B., ‘The structure of almost-invariant half-spaces for some operators’, J. Funct. Anal. 267 (2014), 22982312.
[7] Sirotkin, G. and Wallis, B., ‘Almost-invariant and essentially-invariant half-spaces’, Linear Algebra Appl. 507 (2016), 399413.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

MSC classification

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