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ALMOST INVARIANT HALF-SPACES FOR OPERATORS ON HILBERT SPACE

Part of: General theory of linear operators

Published online by Cambridge University Press:  31 August 2017

IL BONG JUNG Open the ORCID record for IL BONG JUNG [Opens in a new window] ,
EUNGIL KO  and
CARL PEARCY
IL BONG JUNG*
Affiliation:
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea email [email protected]
EUNGIL KO
Affiliation:
Department of Mathematics, Ewha Womans University, Seoul 120-750, Korea email [email protected]
CARL PEARCY
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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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.

Keywords

invariant subspacehalf-spacealmost invariant half-spacealmost invariant half-space with defect n

MSC classification

Primary: 47A15: Invariant subspaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 133 - 140
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

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).

References

Androulakis, G., Popov, A., Tcaciuc, A. and Troitsky, V., ‘Almost invariant half-spaces of operators on Banach spaces’, Integral Equations Operator Theory 65 (2009), 473–484.CrossRefGoogle Scholar
Bernik, J. and Radjavi, H., ‘Invariant and almost-invariant subspaces for pairs of idempotents’, Integral Equations Operator Theory 84 (2016), 283–288.CrossRefGoogle Scholar
Marcoux, L., Popov, A. and Radjavi, H., ‘On almost-invariant subspaces and approximate commutation’, J. Funct. Anal. 264 (2013), 1088–1111.CrossRefGoogle Scholar
Popov, A., ‘Almost invariant half-spaces of algebras of operators’, Integral Equations Operator Theory 67 (2010), 247–256.CrossRefGoogle Scholar
Popov, A. and Tcaciuc, A., ‘Every operator has almost-invariant subspaces’, J. Funct. Anal. 265 (2013), 257–265.CrossRefGoogle Scholar
Sirotkin, G. and Wallis, B., ‘The structure of almost-invariant half-spaces for some operators’, J. Funct. Anal. 267 (2014), 2298–2312.CrossRefGoogle Scholar
Sirotkin, G. and Wallis, B., ‘Almost-invariant and essentially-invariant half-spaces’, Linear Algebra Appl. 507 (2016), 399–413.CrossRefGoogle Scholar