Compact Toeplitz operators via the Berezin transform on bounded symmetric domains |
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Authors: | Miroslav Engliš |
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Institution: | (1) Mathematical Institute, Academy of Sciences, Zitná 25, 11567 Prague 1, Czech Republic |
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Abstract: | Let be an irreducible bounded symmetric domain of genusp, h(x, y) its Jordan triple determinant, andA
2
() the standard weighted Bergman space of holomorphic functions on square-integrable with respect to the measureh(z, z)
–p
dz. Extending the recent result of Axler and Zheng for =D, =p=2 (the unweighted Bergman space on the unit disc), we show that ifS is a finite sum of finite products of Toeplitz operators onA
2
() and is sufficiently large, thenS is compact if and only if the Berezin transform
ofS tends to zero asz approaches . An analogous assertion for the Fock space is also obtained.The author's research was supported by GA AV R grant A1019701 and GA R grant 201/96/0411. |
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Keywords: | 47B35 32M15 |
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