Details
| Original language | English |
|---|---|
| Pages (from-to) | 645-669 |
| Number of pages | 25 |
| Journal | International Journal of Mathematics |
| Volume | 19 |
| Issue number | 6 |
| Publication status | Published - Jul 2008 |
| Externally published | Yes |
Abstract
For a series of weighted Bergman spaces over bounded symmetric domains in ℂn, it has been shown by Axler and Zheng [1]; Englis [10] that the compactness of Toeplitz operators with bounded symbols can be characterized via the boundary behavior of its Berezin transform Ba. In case of the pluriharmonic Bergman space, the pluriharmonic Berezin transform Bph fails to be one-to-one in general and even has non-compact operators in its kernel. From this point of view, perhaps surprisingly we show that via B ph the same characterization of compactness holds for Toeplitz operators on the pluriharmonic Fock space.
Keywords
- Compact Toeplitz operators, Fock space, Pluriharmonic Berezin transform, Pluriharmonic Bergman space
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: International Journal of Mathematics, Vol. 19, No. 6, 07.2008, p. 645-669.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Compact Operators And The Pluriharmonic Berezin Transform
AU - Bauer, Wolfram
AU - Furutani, Kenro
N1 - Funding Information: The first named author was supported by a JSPS fellowship (PE 05570) for North American and European Researchers. The second named author has been partially supported by the (Grant-in-aid Scientific Research) (C) No. 17540202, Japan Society for Promotion of Science (JSPS). Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/7
Y1 - 2008/7
N2 - For a series of weighted Bergman spaces over bounded symmetric domains in ℂn, it has been shown by Axler and Zheng [1]; Englis [10] that the compactness of Toeplitz operators with bounded symbols can be characterized via the boundary behavior of its Berezin transform Ba. In case of the pluriharmonic Bergman space, the pluriharmonic Berezin transform Bph fails to be one-to-one in general and even has non-compact operators in its kernel. From this point of view, perhaps surprisingly we show that via B ph the same characterization of compactness holds for Toeplitz operators on the pluriharmonic Fock space.
AB - For a series of weighted Bergman spaces over bounded symmetric domains in ℂn, it has been shown by Axler and Zheng [1]; Englis [10] that the compactness of Toeplitz operators with bounded symbols can be characterized via the boundary behavior of its Berezin transform Ba. In case of the pluriharmonic Bergman space, the pluriharmonic Berezin transform Bph fails to be one-to-one in general and even has non-compact operators in its kernel. From this point of view, perhaps surprisingly we show that via B ph the same characterization of compactness holds for Toeplitz operators on the pluriharmonic Fock space.
KW - Compact Toeplitz operators
KW - Fock space
KW - Pluriharmonic Berezin transform
KW - Pluriharmonic Bergman space
UR - http://www.scopus.com/inward/record.url?scp=46049094829&partnerID=8YFLogxK
U2 - 10.1142/S0129167X08004832
DO - 10.1142/S0129167X08004832
M3 - Article
AN - SCOPUS:46049094829
VL - 19
SP - 645
EP - 669
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 6
ER -