Linear sums of two composition operators on the Fock space

Boo Rim Choe; Kou Hei Izuchi; Hyungwoon Koo

doi:10.1016/j.jmaa.2010.02.029

Linear sums of two composition operators on the Fock space

Boo Rim Choe, Kou Hei Izuchi, Hyungwoon Koo

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

28 Citations (Scopus)

Abstract

Linear sums of two composition operators of the multi-dimensional Fock space are studied. We show that such an operator is bounded only when both composition operators in the sum are bounded. So, cancelation phenomenon is not possible on the Fock space, in contrast to what have been known on other well-known function spaces over the unit disk. We also show the analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators the investigation is left open.

Original language	English
Pages (from-to)	112-119
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	369
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2010.02.029
Publication status	Published - 2010 Sept

Keywords

Composition operator
Fock space
Linear sum

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2010.02.029

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abstract = "Linear sums of two composition operators of the multi-dimensional Fock space are studied. We show that such an operator is bounded only when both composition operators in the sum are bounded. So, cancelation phenomenon is not possible on the Fock space, in contrast to what have been known on other well-known function spaces over the unit disk. We also show the analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators the investigation is left open.",

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N2 - Linear sums of two composition operators of the multi-dimensional Fock space are studied. We show that such an operator is bounded only when both composition operators in the sum are bounded. So, cancelation phenomenon is not possible on the Fock space, in contrast to what have been known on other well-known function spaces over the unit disk. We also show the analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators the investigation is left open.

AB - Linear sums of two composition operators of the multi-dimensional Fock space are studied. We show that such an operator is bounded only when both composition operators in the sum are bounded. So, cancelation phenomenon is not possible on the Fock space, in contrast to what have been known on other well-known function spaces over the unit disk. We also show the analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators the investigation is left open.

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KW - Linear sum

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Linear sums of two composition operators on the Fock space

Abstract

Keywords

ASJC Scopus subject areas

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