Abstract
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.
Highlights
Let m ∈ N, the one-dimensional m poly-Fock space F2mðCÞ ⊂ L2ðC, dμÞ consists of all m-analytic functions φ which satisfy ∂ m ∂z φ = ∂ ∂x + i∂ m ∂y φ ð1Þ where dμ = π−1e−z·z dxdy is the Gaussian measure in C and d xdy is the Euclidian measure in R2 = C
In [4], the authors studied Toeplitz operators acting on the one-dimensional polyFock space with horizontal symbols such that the limit values at x = ∞ and x = −∞ exist
The main result of this paper is the following: the C∗-algebra generated by Toeplitz operators with extended Lagrangian symbols acting on the homogeneously poly-Fock space over Cn is isomorphic and isometric to the C∗-algebra of matrix-valued functions on a certain compactification of Rn with the sphere at the infinity; the values at the infinity points are scalar multiplies of the identity matrix
Summary
Let m ∈ N, the one-dimensional m poly-Fock space F2mðCÞ ⊂ L2ðC, dμÞ consists of all m-analytic functions φ which satisfy. In [4], the authors studied Toeplitz operators acting on the one-dimensional polyFock space with horizontal symbols such that the limit values at x = ∞ and x = −∞ exist They proved that the C∗-algebra generated with this class of symbols is isomorphic to the C∗-algebra of functions on R with values on the m × m matrices, whose limit value at x = ∞ and x = −∞ are equal to some scalar multiples of the identity matrix. The main result of this paper is the following: the C∗-algebra generated by Toeplitz operators with extended Lagrangian symbols acting on the homogeneously poly-Fock space over Cn is isomorphic and isometric to the C∗-algebra of matrix-valued functions on a certain compactification of Rn with the sphere at the infinity; the values at the infinity points are scalar multiplies of the identity matrix.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
