Browse > Article
http://dx.doi.org/10.5831/HMJ.2017.39.2.175

FREDHOLM TOEPLITZ OPERATORS ON THE PLURIHARMONIC DIRICHLET SPACE  

Lee, Young Joo (Department of Mathematics, Chonnam National University)
Publication Information
Honam Mathematical Journal / v.39, no.2, 2017 , pp. 175-185 More about this Journal
Abstract
In this paper we consider Toeplitz operators on the pluriharmonic Dirichlet space of the unit ball in the n-dimensional complex space. We then characterize Fredholm Toeplitz operators and describe the essential spectrum of a Toeplitz operator as a consequence.
Keywords
Toeplitz operator; pluriharmonic Dirichlet space; Fredholm operator;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. Adams, Sobolev Spaces, Academic press, New York, 1975.
2 G. Cao, Fredholm properties of Toeplitz operators on Dirichlet spaces, Pacific J. Math. 188 (1999) 209-223.   DOI
3 J. B. Conway, A Course in Operator Theory, Amer. Math. Soc. Providence, Rhode Island, 1999.
4 R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
5 Y. J. Lee, Compact sums of Toeplitz products and Toeplitz algebra on the Dirichlet space, Tohoku Math. J., 68 (2016) 253-271.   DOI
6 G. McDonald, Fredholm properties of a class of Toeplitz operators on the ball, Indiana Univ. Math. J., 26 (1977) 567-576.   DOI
7 W. Rudin, Function Theory in the Unit Ball of ${\mathbb{C}}^n$, Springer-Verlag, New York, 1980.
8 K. Zhu, Space of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.