Algebra Generated by a Finite Number of Toeplitz Operators with Homogeneous Symbols Acting on the Poly-Bergman Spaces

Ramírez-Mora, María del Rosario; Ortega, Josué Ramírez; Morales-Ramos, Miguel Antonio

doi:10.1007/978-3-030-44651-2_22

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…By analogy to [30,32], it is natural to conjecture that X n,α can be generated by a finite set of matrix sequences γ n,α (a) with a in L ∞ lim ([0, 1)), but we have not proved (or disproved) this conjecture.…”

Section: Introduction and Main Resultsmentioning

confidence: 80%

“…The authors of these papers used the technique of pure state separation and Kaplansky's noncommutative analog of Stone-Weierstrass theorem [19]. We also mention other papers about Toeplitz operators acting in polyanalytic Bergman spaces [6,14,17,30,33,37].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…The difficult part is to show that G n,α is sufficiently rich to generate L n . Following Loaiza and Lozano [21] and other papers [23,[30][31][32]34], we use the concept of pure states and apply Kaplansky's noncommutative analog of Stone-Weierstrass theorem to prove that X n,α = L n .…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Radial operators on polyanalytic weighted Bergman spaces

Barrera-Castelán

Maximenko

Ramos-Vazquez

2021

Bol. Soc. Mat. Mex.

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In a previous paper (Radial operators on polyanalytic weighted Bergman spaces, Bol. Soc. Mat. Mex. 27, 43), using disk polynomials as an orthonormal basis in the n-analytic weighted Bergman space, we showed that for every bounded radial generating symbol a, the associated Toeplitz operator, acting in this space, can be identified with a matrix sequence γ(a), where the entries of the matrices are certain integrals involving a and Jacobi polynomials. In this paper, we suppose that the generating symbols a have finite limits on the boundary and prove that the C*-algebra generated by the corresponding matrix sequences γ(a) is the C*-algebra of all matrix sequences having scalar limits at infinity. We use Kaplansky's noncommutative analog of the Stone-Weierstrass theorem and some ideas from several papers by Loaiza, Lozano, Ramírez-Ortega, Ramírez-Mora, and Sánchez-Nungaray. We also prove that for n ≥ 2, the closure of the set of matrix sequences γ(a) is not equal to the generated C*-algebra.

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Section: Introduction and Main Resultsmentioning

confidence: 80%

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Radial operators on polyanalytic weighted Bergman spaces

Barrera-Castelán

Maximenko

Ramos-Vazquez

2021

Bol. Soc. Mat. Mex.

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“…Taking vertical symbols having limit values at y = 0 and y = ∞, in [14] the authors found that R + = [0, +∞] is the spectrum of the algebra generated by all Toeplitz operators on the true-poly Bergman space A 2 (n) (Π). Similar research was made for Toeplitz operators on poly-Bergman spaces with homogeneous symbols ( [11,17]). Other works about it were made in [9,10,16], where the authors studied Toeplitz operators acting on A 2 (n) (Π) from the point of view of wavelet spaces.…”

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confidence: 73%

Toeplitz Operators Acting on True-Poly-Bergman Type Spaces of the Two-Dimensional Siegel Domain: Nilpotent Symbols

Hernández-Eliseo

Ortega

Hernández-Zamora

2021

Journal of Function Spaces

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We describe certain C ∗ -algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain D 2 ⊂ ℂ 2 . Bounded measurable functions of the form c Im ζ 1 , Im ζ 2 − ζ 1 2 are called nilpotent symbols. In this work, we consider symbols of the form a Im ζ 1 b Im ζ 2 − ζ 1 2 , where both limits lim s → 0 + b s and lim s → + ∞ b s exist, and a s belongs to the set of piecewise continuous functions on ℝ ¯ = − ∞ , + ∞ and having one-side limit values at each point of a finite set S ⊂ ℝ . We prove that the C ∗ -algebra generated by all Toeplitz operators T a b is isomorphic to C Π ¯ , where Π ¯ = ℝ ¯ × ℝ ¯ + and ℝ ¯ + = 0 , + ∞ .

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