Browse > Article
http://dx.doi.org/10.5831/HMJ.2019.41.3.619

ESSENTIAL NORMS OF SUMS OF TOEPLITZ PRODUCTS ON THE PLURIHARMONIC DIRICHLET SPACE  

Lee, Young Joo (Department of Mathematics, Chonnam National University)
Publication Information
Honam Mathematical Journal / v.41, no.3, 2019 , pp. 619-629 More about this Journal
Abstract
On the setting of the pluriharmonic Dirichlet space, we describe the essential norm of an operator which is a finite sum of products of several Toeplitz operators.
Keywords
Toeplitz operator; pluriharmonic Dirichlet space; Essential norm;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 R. Adams, Sobolev Spaces, Academic press, New York, 1975.
2 S. Axler and D. Zheng, Compact operators via the Berezin transform, Indiana Univ. Math. J., 47 (1998) 387-400.
3 B. R. Choe, H. Koo and Y. J. Lee, Toeplitz products with pluriharmonic symbols on the Hardy space over the ball, J. of Mathematical Analysis and Application, 381 (2011) 365-382.   DOI
4 B. R. Choe, H. Koo and Y. J. Lee, Zero products of Toeplitz operators with n-harmonic symbols, Integral Equation and Operator Theory, 57 (2007) 43-66.   DOI
5 M. Englis, Compact Toeplitz operators via the Berezin transform on bounded symmetric domains, Integral Equation and Operator Theory, 33 (1999) 426-455.   DOI
6 C. K. Fong, On the essential maximal numerical range, Acta Sci. Math., 41 (1979) 307-315.
7 Y. J. Lee, Compact sums of Toeplitz products and Toeplitz algebra on the Dirichlet space, Tohoku Math. J., 68 (2016) 253-271.   DOI
8 Y. J. Lee, Fredholm Toeplitz operators on the pluriharmonic Dirichlet space, Honam Mathematical J., 39 (2017) 175-185.   DOI
9 Y. J. Lee and K. Na, The essential norm of a sum of Toeplitz products on the Dirichlet space, J. of Mathematical Analysis and Application, 431 (2015) 1022-1034.   DOI
10 W. Rudin, Function Theory in the Unit Ball of ${\mathbb{C}}^n$, Springer-Verlag, New York, 1980.