scholarly journals Toeplitz Operators with I M O s Symbols between Generalized Fock Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yiyuan Zhang ◽  
Guangfu Cao ◽  
Li He
Keyword(s):  
Toeplitz Operators ◽  
Fock Space ◽  
Fock Spaces

In this paper, we study the mapping properties of Toeplitz operators T f associated with IMO s   symbols f acting between two generalized Fock spaces F φ p , where 1 < s ≤ ∞ . We characterize bounded or compact Toeplitz operators T f from one generalized Fock space F φ p to another F φ q , respectively, in four cases.

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

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Armando Sánchez-Nungaray ◽  
Carlos González-Flores ◽  
Raquiel Rufino López-Martínez ◽  
Jorge Luis Arroyo-Neri
Keyword(s):  
Complex Plane ◽  
Gaussian Measure ◽  
Toeplitz Operators ◽  
Fock Space ◽  
Identity Matrix ◽  
Fock Spaces ◽  
Limit Values ◽  
Bounded Functions

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.

scholarly journals CUMULANTS IN NONCOMMUTATIVE PROBABILITY THEORY III: CREATION AND ANNIHILATION OPERATORS ON FOCK SPACES

2005 ◽  
Vol 08 (03) ◽  
pp. 407-437 ◽  
Author(s):  
FRANZ LEHNER
Keyword(s):  
Probability Theory ◽  
Symmetric Group ◽  
Toeplitz Operators ◽  
Fock Space ◽  
Random Variables ◽  
Fock Spaces ◽  
Noncommutative Probability ◽  
Infinite Symmetric Group ◽  
Fock States ◽  
Cycle Indicator

Exchangeability systems arising from Fock space constructions are considered and the corresponding cumulants are computed for generalized Toeplitz operators and similar noncommutative random variables. In particular, simplified calculations are given for the two known examples of q-cumulants. In the second half of the paper we consider in detail the Fock states associated to characters of the infinite symmetric group recently constructed by Bożejko and Guta. We express moments of multidimensional Dyck words in terms of the so-called cycle indicator polynomials of certain digraphs.

scholarly journals Toeplitz operators between large Fock spaces in several complex variables

2021 ◽  
Vol 7 (1) ◽  
pp. 1293-1306
Author(s):  
Ermin Wang ◽  
◽  
Jiajia Xu
Keyword(s):  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Borel Measure ◽  
Fock Space ◽  
Holomorphic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Weight Class ◽  
Fock Spaces ◽  
Positive Borel Measure

<abstract><p>Let $ \omega $ belong to the weight class $ \mathcal{W} $, the large Fock space $ \mathcal{F}_{\omega}^{p} $ consists of all holomorphic functions $ f $ on $ \mathbb{C}^{n} $ such that the function $ f(\cdot)\omega(\cdot)^{1/2} $ is in $ L^p(\mathbb{C}^{n}, dv) $. In this paper, given a positive Borel measure $ \mu $ on $ {\mathbb C}^n $, we characterize the boundedness and compactness of Toeplitz operator $ T_\mu $ between two large Fock spaces $ F^{p}_\omega $ and $ F^{q}_\omega $ for all possible $ 0 &lt; p, q &lt; \infty $.</p></abstract>

Toeplitz Operators on the Fock Space with Presymbols Discontinuous on a Thick Set

1996 ◽  
Vol 180 (1) ◽  
pp. 299-315 ◽  
Author(s):  
E. Ram Írez De Arellano ◽  
N. L. Vasilevski
Keyword(s):  
Toeplitz Operators ◽  
Fock Space

scholarly journals Factorization of the canonical bases for higher-level Fock spaces

2011 ◽  
Vol 55 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Susumu Ariki ◽  
Nicolas Jacon ◽  
Cédric Lecouvey
Keyword(s):  
Fock Space ◽  
Fock Spaces ◽  
Transition Matrices ◽  
Canonical Bases ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Graphic Module ◽  
Module Structures ◽  
Weight Modules

AbstractThe level l Fock space admits canonical bases $\mathcal{G}_{e}$ and $\smash{\mathcal{G}_{\infty}}$. They correspond to $\smash{\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})}$ and $\mathcal{U}_{v}({\mathfrak{sl}}_{\infty})$-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[v]. Restriction to the highest-weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki–Koike algebras.

scholarly journals Toeplitz Operators with Lagrangian Invariant Symbols Acting on the Poly-Fock Space of ℂ n

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jorge Luis Arroyo Neri ◽  
Armando Sánchez-Nungaray ◽  
Mauricio Hernández Marroquin ◽  
Raquiel R. López-Martínez
Keyword(s):  
Toeplitz Operators ◽  
Complex Space ◽  
Fock Space ◽  
Identity Matrix ◽  
The Matrix

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.

scholarly journals Interacting Fock spaces and subproduct systems

2020 ◽  
Vol 23 (03) ◽  
pp. 2050017
Author(s):  
Malte Gerhold ◽  
Michael Skeide
Keyword(s):  
Selfadjoint Operator ◽  
Operator Algebras ◽  
Fock Space ◽  
Fock Spaces ◽  
Full Generality ◽  
Necessary And Sufficient Criteria ◽  
Definition Of ◽  
Interacting Fock Space ◽  
Necessary And Sufficient

We present a new more flexible definition of interacting Fock space that allows to resolve in full generality the problem of embeddability. We show that the same is not possible for regularity. We apply embeddability to classify interacting Fock spaces by squeezings. We give necessary and sufficient criteria for when an interacting Fock space has only bounded creators, giving thus rise to new classes of non-selfadjoint and selfadjoint operator algebras.

scholarly journals Deformed Fock spaces, Hecke operators and monotone Fock space of Muraki

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Marek Bożejko
Keyword(s):  
Fock Space ◽  
Hecke Operators ◽  
Fock Spaces

AbstractThe main purpose of this paper is to extend our previous construction of

Schatten-p class (0 < p ≤ ∞) Toeplitz operators on generalized Fock spaces

2015 ◽  
Vol 31 (4) ◽  
pp. 703-714 ◽  
Author(s):  
Lian Hua Xiao ◽  
Xiao Feng Wang ◽  
Jin Xia
Keyword(s):  
Toeplitz Operators ◽  
Fock Spaces
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