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Fredholm Toeplitz operators on the Dirichlet spaces of the polydisk

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We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.

Abstract

We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.

참고문헌 (10)

  1. R. A. Adams, "Sobolev Spaces" (1975), Academic Press
  2. Guangfu Cao, "Fredholm properties of Toeplitz operators on Dirichlet spaces", Pacific Journal of Mathematics, 188(2), pp.209~223 (1999), Mathematical Sciences Publishers[DOI]
  3. Boo Rim Choe, "Commuting Toeplitz operators on the polydisk", Transactions of the American Mathematical Society, 356(5), pp.1727~1749 (2004), American Mathematical Society (AMS)[DOI]
  4. J. B. Conway, "A Course in Operator Theory" (2000), American Mathematical Society
  5. Y. J. Lee, "Compact sums of Toeplitz products and Toeplitz algebra on the Dirichlet space", Tohoku Math. J, 68(2), pp.253~271 (2016)
  6. 이영주, "Fredholm Toeplitz operators on the pluriharmonic Dirichlet space", 호남수학학술지, 39(2), pp.175~185 (2017), 호남수학회
  7. Young Joo Lee, "The essential norm of a sum of Toeplitz products on the Dirichlet space", Journal of Mathematical Analysis and Applications, 431(2), pp.1022~1034 (2015), Elsevier BV[DOI]
  8. Gerard McDonald, "Fredholm properties of a class of Toeplitz operators on the ball", Indiana University Mathematics Journal, 26(3), pp.567~576 (1977), Indiana University Mathematics Journal[DOI]
  9. W. Rudin, "Springer-Verlag" (1980), Springer-Verlag
  10. K. Zhu, "Spaces of Holomorphic Functions in the Unit Ball" (2005), Springer-Verlag

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