ORIGINAL ARTICLE
Fredholm theory of the Toeplitz algebra on the space of all entire functions
M. Jasiczak,
Corresponding Author
M. Jasiczak
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Correspondence
M. Jasiczak, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland.
Email: [email protected]
Search for more papers by this authorM. Jasiczak,
Corresponding Author
M. Jasiczak
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Correspondence
M. Jasiczak, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland.
Email: [email protected]
Search for more papers by this authorFirst published: 07 June 2024
Abstract
We prove that an aggregate Toeplitz operator on the Fréchet space of all entire functions is a Fredholm operator if and only if its symbol does not vanish. The result is motivated by and closely resembles the classical result of Gohberg and Douglas from the Hardy space theory of Toeplitz operators. There are however some subtle differences which we also discuss.
CONFLICT OF INTEREST STATEMENT
The author declares no conflicts of interest.
Open Research
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