Toeplitz Quantization for Non-commutating Symbol Spaces such as $SU_q(2)$

Stephen Bruce Sontz

Displaying similar documents to “Toeplitz Quantization for Non-commutating Symbol Spaces such as $S U_{q} (2)$ ”

Notes on unbounded Toeplitz operators in Segal-Bargmann spaces

D. Cichoń (1996)

Annales Polonici Mathematici

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Relations between different extensions of Toeplitz operators $T_{φ}$ are studied. Additive properties of closed Toeplitz operators are investigated, in particular necessary and sufficient conditions are given and some applications in case of Toeplitz operators with polynomial symbols are indicated.

Generalization of the Newman-Shapiro isometry theorem and Toeplitz operators. II

Dariusz Cichoń (2002)

Studia Mathematica

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The Newman-Shapiro Isometry Theorem is proved in the case of Segal-Bargmann spaces of entire vector-valued functions (i.e. summable with respect to the Gaussian measure on ℂⁿ). The theorem is applied to find the adjoint of an unbounded Toeplitz operator $T_{φ}$ with φ being an operator-valued exponential polynomial.

Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht Böttcher, Hartmut Wolf (1997)

Banach Center Publications

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Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk $^{N}$ or on the Segal-Bargmann space over $ℂ^{N}$ . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression $A_{n}$ of A to the linear span of the monomials $z_{1}^{k_{1}} . . . z_{N}^{k_{N}} : 0 \leq k_{j} \leq n$ . Unfortunately, in general the spectrum of $A_{n}$ does not mimic the spectrum...

Product equivalence of quasihomogeneous Toeplitz operators on the harmonic Bergman space

Xing-Tang Dong, Ze-Hua Zhou (2013)

Studia Mathematica

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We present here a quite unexpected result: If the product of two quasihomogeneous Toeplitz operators $T_{f} T_{g}$ on the harmonic Bergman space is equal to a Toeplitz operator $T_{h}$ , then the product $T_{g} T_{f}$ is also the Toeplitz operator $T_{h}$ , and hence $T_{f}$ commutes with $T_{g}$ . From this we give necessary and sufficient conditions for the product of two Toeplitz operators, one quasihomogeneous and the other monomial, to be a Toeplitz operator.

Toeplitz operators, Kähler manifolds, and line bundles.

Foth, Tatyana (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Bounded Toeplitz and Hankel products on weighted Bergman spaces of the unit ball

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2010)

Annales Polonici Mathematici

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We prove a sufficient condition for products of Toeplitz operators $T_{f} T_{ḡ}$ , where f,g are square integrable holomorphic functions in the unit ball in ℂⁿ, to be bounded on the weighted Bergman space. This condition slightly improves the result obtained by K. Stroethoff and D. Zheng. The analogous condition for boundedness of products of Hankel operators $H_{f} H *_{g}$ is also given.

Schatten class Toeplitz operators acting on large weighted Bergman spaces

Hicham Arroussi, Inyoung Park, Jordi Pau (2015)

Studia Mathematica

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A full description of the membership in the Schatten ideal $S_{p} (A ²_{ω})$ for 0 < p < ∞ of Toeplitz operators acting on large weighted Bergman spaces is obtained.

The essential spectrum of Toeplitz tuples with symbols in $H^{\infty} + C$

Jörg Eschmeier (2013)

Studia Mathematica

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Let H²(D) be the Hardy space on a bounded strictly pseudoconvex domain D ⊂ ℂⁿ with smooth boundary. Using Gelfand theory and a spectral mapping theorem of Andersson and Sandberg (2003) for Toeplitz tuples with $H^{\infty}$ -symbol, we show that a Toeplitz tuple $T_{f} = (T_{f ₁}, . . ., T_{f ₘ}) \in L {(H ² (σ))}^{m}$ with symbols $f_{i} \in H^{\infty} + C$ is Fredholm if and only if the Poisson-Szegö extension of f is bounded away from zero near the boundary of D. Corresponding results are obtained for the case of Bergman spaces. Thus we extend results of McDonald (1977) and...

Slant Hankel operators

Subhash Chander Arora, Ruchika Batra, M. P. Singh (2006)

Archivum Mathematicum

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In this paper the notion of slant Hankel operator $K_{ϕ}$ , with symbol $ϕ$ in $L^{\infty}$ , on the space $L^{2} (𝕋)$ , $𝕋$ being the unit circle, is introduced. The matrix of the slant Hankel operator with respect to the usual basis ${z^{i} : i \in ℤ}$ of the space $L^{2}$ is given by $〈 α_{i j} 〉 = 〈 a_{- 2 i - j} 〉$ , where $\sum_{i = - \infty}^{\infty} a_{i} z^{i}$ is the Fourier expansion of $ϕ$ . Some algebraic properties such as the norm, compactness of the operator $K_{ϕ}$ are discussed. Along with the algebraic properties some spectral properties of such operators are discussed. Precisely, it is proved that for...

Deformation quantization and Borel's theorem in locally convex spaces

Miroslav Engliš, Jari Taskinen (2007)

Studia Mathematica

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It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth...

The K-theory of the triple-Toeplitz deformation of the complex projective plane

Jan Rudnik (2012)

Banach Center Publications

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$π_{j}^{i} : B_{i} \to B_{i j} = B_{j i}$ , i,j ∈ 1,2,3, i ≠ j, of C*-epimorphisms assuming that it satisfies the cocycle condition. Then we show how to compute the K-groups of the multi-pullback C*-algebra of such a family, and exemplify it in the case of the triple-Toeplitz deformation of ℂP².

On Pták’s generalization of Hankel operators

Carmen H. Mancera, Pedro José Paúl (2001)

Czechoslovak Mathematical Journal

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In 1997 Pták defined generalized Hankel operators as follows: Given two contractions $T_{1} \in ℬ (ℋ_{1})$ and $T_{2} \in ℬ (ℋ_{2})$ , an operator $X ℋ_{1} \to ℋ_{2}$ is said to be a generalized Hankel operator if $T_{2} X = X T_{1}^{*}$ and $X$ satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of $T_{1}$ and $T_{2}$ . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong...

Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.

Noncirculant Toeplitz matrices all of whose powers are Toeplitz

Kent Griffin, Jeffrey L. Stuart, Michael J. Tsatsomeros (2008)

Czechoslovak Mathematical Journal

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Let $a$ , $b$ and $c$ be fixed complex numbers. Let $M_{n} (a, b, c)$ be the $n \times n$ Toeplitz matrix all of whose entries above the diagonal are $a$ , all of whose entries below the diagonal are $b$ , and all of whose entries on the diagonal are $c$ . For $1 \leq k \leq n$ , each $k \times k$ principal minor of $M_{n} (a, b, c)$ has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of $M_{n} (a, b, c)$ . We also show that all complex polynomials in $M_{n} (a, b, c)$ are Toeplitz matrices. In particular, the inverse of $M_{n} (a, b, c)$ is a Toeplitz...

Compact operators on the weighted Bergman space A¹(ψ)

Tao Yu (2006)

Studia Mathematica

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We show that a bounded linear operator S on the weighted Bergman space A¹(ψ) is compact and the predual space A₀(φ) of A¹(ψ) is invariant under S* if and only if $S k_{z} \to 0$ as z → ∂D, where $k_{z}$ is the normalized reproducing kernel of A¹(ψ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.

Displaying similar documents to “Toeplitz Quantization for Non-commutating Symbol Spaces such as S U q ( 2 ) ”

Displaying similar documents to “Toeplitz Quantization for Non-commutating Symbol Spaces such as $S U_{q} (2)$ ”