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On Fredholm properties of Toeplitz operators in Bergman spaces
Author(s) -
Taskinen Jari,
Virtanen Jani
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6268
Subject(s) - toeplitz matrix , mathematics , bergman space , compact space , pure mathematics , integrable system , toeplitz operator , operator theory , fredholm theory , complex plane , order (exchange) , unit disk , unit (ring theory) , mathematical analysis , algebra over a field , fredholm integral equation , integral equation , bounded function , mathematics education , finance , economics
We consider Toepliz operators with integrable symbols acting on Bergman spacesA p , 1 < p < ∞ , of the open unit disc of the complex plane. We combine some of the best known results on compactness of Toeplitz and Hankel operators in order to generalize the results on Fredholm properties of Toeplitz operators. We pay special attention to some concrete examples.