Toeplitz Operators with Lagrangian Invariant Symbols Acting on the Poly-Fock Space of
ℂ
n
We introduce the so-called extended Lagrangian symbols, and we prove that the C ∗ -algebra generated by Toeplitz operators with these kind of symbols acting on the homogeneously poly-Fock space of the complex space ℂ n is isomorphic and isometric to the C ∗ -algebra of matrix-valued functions on a certain compactification of ℝ n obtained by adding a sphere at the infinity; moreover, the matrix values at the infinity points are equal to some scalar multiples of the identity matrix.
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1996 ◽
Vol 180
(1)
◽
pp. 299-315
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1998 ◽
Vol 13
(34)
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pp. 2731-2742
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2003 ◽
Vol 2003
(34)
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pp. 2157-2176
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2015 ◽
Vol 12
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pp. 1-13
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2019 ◽
Vol 150
(6)
◽
pp. 3163-3186
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