Fredholm Toeplitz operators on the Dirichlet spaces of the polydisk
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 509-520
https://doi.org/10.4134/BKMS.b190371
Published online March 31, 2020
Kyunguk Na
Hanshin University
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.
Keywords : Toeplitz operator, Dirichlet space, pluriharmonic Dirichlet space, Fredholm operator
MSC numbers : Primary 47B35; Secondary 32A37
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