Toeplitz Localization Operators: Spectral Functions Density

Hutník, Ondrej; Maximenko, Egor A.; Mišková, Anna

doi:10.1007/s11785-016-0564-1

Cited by 9 publications

(5 citation statements)

References 24 publications

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“…Hutník, Hutníková, Ramírez Ortega, Sánchez-Nungaray, Loaiza, and other authors [18,19,23,26,29] studied vertical and angular Toeplitz operators in polyanalytic and truepolyanalytic spaces, Bergman and Fock. In particular, vertical Toeplitz operators in the n-analytic Bergman space over the upper half-plane are represented in [26] as n×n matrices whose entries are continuous functions on (0, +∞), with some additional properties at 0 and +∞.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Maximenko,

Tellería-Romero

2019

Preprint

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The paper considers bounded linear radial operators on the polyanalytic Fock spaces F n and on the true-polyanalytic Fock spaces F (n) . The orthonormal basis of normalized complex Hermite polynomials plays a crucial role in this study; it can be obtained by the orthogonalization of monomials in z and z. First, using this basis, we decompose the von Neumann algebra of radial operators, acting in F n , into the direct sum of some matrix algebras, i.e. radial operators are represented as matrix sequences. Secondly, we prove that the radial operators, acting in F (n) , are diagonal with respect to the basis of the complex Hermite polynomials belonging to F (n) . We also provide direct proofs of the fundamental properties of F n and an explicit description of the C*-algebra generated by Toeplitz operators in F (n) , whose generating symbols are radial, bounded, and have finite limits at infinity.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Maximenko,

Tellería-Romero

2019

Preprint

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“…For example, in [3], Sánchez-Nungaray and Vasilevski studied Toeplitz operators with pseudodifferential symbols acting on poly-Bergman spaces upper half plane. A different approach by Hutník, Maximenko, and Mišková in [4] considers Toeplitz Localization operators on the space of Wavelet transform or the space of short-time Fourier 2 Journal of Function Spaces transform. They studied these operators with symbols that just depend on the first coordinate in the phase space, which are unitary equivalent to multiplication operators of certain specific functions "spectral functions".…”

Section: (C −| |mentioning

confidence: 99%

Toeplitz Operators with Horizontal Symbols Acting on the Poly-Fock Spaces

Sánchez-Nungaray

Gonzalez-Flores

López-Martínez

et al. 2018

Journal of Function Spaces

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We describe the C⁎-algebra generated by the Toeplitz operators acting on each poly-Fock space of the complex plane C with the Gaussian measure, where the symbols are bounded functions depending only on x=Re z and have limit values at y=-∞ and y=∞. The C⁎ algebra generated with this kind of symbols is isomorphic to the C⁎-algebra functions on extended reals with values on the matrices of dimension n×n, and the limits at y=-∞ and y=∞ are scalar multiples of the identity matrix.

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“…In these cases approximate inverses for some particular convolutions have been constructed. In particular, the main step in recent papers [18,28,29,32] was to construct an appropriate Dirac net, and using this net to show a density result of a function algebra under consideration in certain C*-algebra (e.g., the algebra SO(N), or the algebra VSO(R + )). An idea of Wiener deconvolution technique on the real line has already been elaborated in [32].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the main step in recent papers [18,28,29,32] was to construct an appropriate Dirac net, and using this net to show a density result of a function algebra under consideration in certain C*-algebra (e.g., the algebra SO(N), or the algebra VSO(R + )). An idea of Wiener deconvolution technique on the real line has already been elaborated in [32]. Immediately we have observed that the used techniques may be generalized to non-unital normed algebras leading to the concept of approximate invertibility as introduced in the paper.…”

Section: Introductionmentioning

confidence: 99%

Approximately invertible elements in non-unital normed algebras

Esmeral¹,

Feichtinger²,

Hutník³

et al. 2021

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We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct extension of topological invertibility to non-unital algebras. Basic observations relate approximate invertibility with concepts of topological divisors of zero and density of (modular) ideals. We exemplify approximate invertibility in the group algebra, Wiener algebras, and operator ideals. For Wiener algebras with approximate identities (in particular, for the Fourier image of the convolution algebra), the approximate invertibility of an algebra element is equivalent to the property that it does not vanish. We also study approximate invertibility and its deeper connection with the Gelfand and representation theory in non-unital abelian Banach algebras as well as abelian and non-abelian C*-algebras. MSC (2020): 46H10, 46L05, 43A20.

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Toeplitz Localization Operators: Spectral Functions Density

Cited by 9 publications

References 24 publications

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Radial operators on polyanalytic Bargmann-Segal-Fock spaces

Toeplitz Operators with Horizontal Symbols Acting on the Poly-Fock Spaces

Approximately invertible elements in non-unital normed algebras

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