A note on the multivariable Berger-Shaw theorem

Rongwei Yang; Yixin Yang

A note on the multivariable Berger-Shaw theorem

Rongwei Yang
, Yixin Yang

Mathematics and Statistics

University at Albany

SUNY Albany

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

Abstract

For a m-cyclic hyponormal operator T, the Berger-Shaw theorem states that tr[T∗; T] is dominated by a scalar multiple of m. This paper uses an example to show that this kind of dominance is unlikely to exist in multivariable cases. The example uses an inner-sequence-based invariant subspace in Hardy space over the bidisc.

Original language	English
Pages (from-to)	273-278
Number of pages	6
Journal	Houston Journal of Mathematics
Volume	41
Issue number	1
State	Published - 2015

Keywords

Core operator
Hardy space over the bidisc
Inner-sequence-based invariant subspace
Joint hyponormal

Cite this

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title = "A note on the multivariable Berger-Shaw theorem",

abstract = "For a m-cyclic hyponormal operator T, the Berger-Shaw theorem states that tr[T∗; T] is dominated by a scalar multiple of m. This paper uses an example to show that this kind of dominance is unlikely to exist in multivariable cases. The example uses an inner-sequence-based invariant subspace in Hardy space over the bidisc.",

keywords = "Core operator, Hardy space over the bidisc, Inner-sequence-based invariant subspace, Joint hyponormal",

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T1 - A note on the multivariable Berger-Shaw theorem

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AU - Yang, Yixin

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AB - For a m-cyclic hyponormal operator T, the Berger-Shaw theorem states that tr[T∗; T] is dominated by a scalar multiple of m. This paper uses an example to show that this kind of dominance is unlikely to exist in multivariable cases. The example uses an inner-sequence-based invariant subspace in Hardy space over the bidisc.

KW - Core operator

KW - Hardy space over the bidisc

KW - Inner-sequence-based invariant subspace

KW - Joint hyponormal

UR - https://www.scopus.com/pages/publications/84929166983

M3 - Article

SN - 0362-1588

VL - 41

SP - 273

EP - 278

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

IS - 1

ER -

A note on the multivariable Berger-Shaw theorem

Abstract

Keywords

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