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- W4283731982 abstract "Abstract We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and Hardy spaces over the unit ball in $$mathbb {C}^n$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> . As an application we discuss semi-simplicity and the spectral invariance of these algebras. The different function Hilbert spaces are dealt with in parallel in successive chapters so that a direct comparison of the results is possible. As a new aspect of the theory we define commutative Toeplitz algebras over spaces of functions in infinitely many variables and present some structural results. The paper concludes with a short list of open problems in this area of research." @default.
- W4283731982 created "2022-07-01" @default.
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- W4283731982 date "2022-06-30" @default.
- W4283731982 modified "2023-10-14" @default.
- W4283731982 title "Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results" @default.
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- W4283731982 doi "https://doi.org/10.1007/s11785-022-01248-1" @default.
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