On operators with similar positive parts

Eungil Ko

doi:10.1016/j.jmaa.2018.03.032

On operators with similar positive parts

Eungil Ko

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let S=U_S|S| and T=U_T|T| be the polar decompositions of S and T in L(H), respectively. We say that S and T have similar positive parts if |S| and |T| are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption.

Original language	English
Pages (from-to)	276-293
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	463
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.03.032
State	Published - 1 Jul 2018

Bibliographical note

Funding Information:
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (2016R1D1A1B03931937).

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Polar decomposition
Similarity of positive parts
Spectral property

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10.1016/j.jmaa.2018.03.032

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abstract = "Let S=US|S| and T=UT|T| be the polar decompositions of S and T in L(H), respectively. We say that S and T have similar positive parts if |S| and |T| are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption.",

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author = "Eungil Ko",

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N2 - Let S=US|S| and T=UT|T| be the polar decompositions of S and T in L(H), respectively. We say that S and T have similar positive parts if |S| and |T| are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption.

AB - Let S=US|S| and T=UT|T| be the polar decompositions of S and T in L(H), respectively. We say that S and T have similar positive parts if |S| and |T| are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption.

KW - Polar decomposition

KW - Similarity of positive parts

KW - Spectral property

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

On operators with similar positive parts

Abstract

Bibliographical note

Keywords

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