Related papers: Star product on $L^2(S^n)$, $n = 2, 3, 5$

We describe the symbolic calculus of operators on the unit sphere in the complex n-space $\mathbb C^n$ defined by the Berezin quantization. In particular, we derive a explicit formula for the composition of Berezin symbol and with that a…

We initiate the study of a class of noncommutative domains of n-tuples of bounded linear operators on a Hilbert space, which is generated by certain positivity conditions on polynomials in n noncommutative indeterminates. We obtain Fatou…

We obtain a new explicit expression for the noncommutative (star) product on the fuzzy two-sphere which yields a unitary representation. This is done by constructing a star product, $\star_{\lambda}$, for an arbitrary representation of…

Let $G$ be a Lie group with Lie algebra $\mathfrak g$ and let $\pi$ be a unitary representation of $G$ realized on a reproducing kernel Hilbert space. We use Berezin quantization to study spectral measures associated with operators…

We give a new construction of symbols of the differential operators on the sections of a quantum line bundle $L$ over a Kaehler manifold $M$ using the natural contravariant connection on $L$. These symbols are the functions on the tangent…

Using the formalism of quantizers and dequantizers, we show that the characters of irreducible unitary representations of finite and compact groups provide kernels for star products of complex-valued functions of the group elements.…

Let $D$ be the irreducible bounded symmetric domain of $2\times2$ complex matrices that satisfy $ZZ^* < I_2$. The biholomorphism group of $D$ is realized by $\mathrm{U}(2,2)$ with isotropy at the origin given by…

This work presents a rigorous characterization of inner products on the Hilbert space $S_2$ of Hilbert--Schmidt operators. We first deal with a general setting of continuous sesquilinear forms on a Hilbert space $\mathcal H$, and provide a…

We present the explicit form of the "hatted star product" within the Cahill-Glauber correspondence framework, which is a commutative mapping of two Hilbert space operators that encodes the quantization prescription. It serves as the…

The approach of Berezin to the quantization of so(n,2) via generalized coherent states is considered in detail. A family of n commuting observables is found in which the basis for an associated Fock-type representation space is expressed.…

The noncommutative star product of phase space functions is, by construction, associative for both non-degenerate and degenerate case (involving only second class constraints) as has been shown by Berezin, Batalin and Tyutin. However, for…

In this paper, we formulate the phase space description of qubit systems using coadjoint orbits of $SU(2)$ and the Stratonovich-Weyl correspondence, yielding a deformation quantization on the sphere. The resulting star product reproduces…

In this paper, by using of the definition Berezin symbol, we show some Berezin number inequalities. Among other inequalities, it is shown that if $A, B, X\in{\mathbb{B}}(\mathscr H)$, then $$\mathbf{ber}(AX\pm XA)\leqslant…

For compact quantizable K\"ahler manifolds certain naturally defined star products and their constructions are reviewed. The presentation centers around the Berezin-Toeplitz quantization scheme which is explained. As star products the…

We show that $\frak{su}(2)$ Lie algebras of coordinate operators related to quantum spaces with $\frak{su}(2)$ noncommutativity can be conveniently represented by $SO(3)$-covariant poly-differential involutive representations. We show that…

Columns of d^2 x N matrices are shown to create different sets of N operators acting on $d$-dimensional Hilbert space. This construction corresponds to a formalism of the star-product of operator symbols. The known bases are shown to be…

We explicitly construct noncommutative * products on circularly symmetric two dimensional space by using the technique of Fedosov's deformation quantization. Especially, on constant curvature spaces i.e., S^2 and H^2, we get su(2) and…

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus…

Lecomte and Ovsienko constructed $SL_{n+1}(R)$-equivariant quantization maps $Q_\lambda$ for symbols of differential operators on $\lambda$-densities on $\RP^n$. We derive some formulas for the associated graded equivariant star products…

The Berezin symbol $\widetilde{A}$ of an operator $A$ acting on the reproducing kernel Hilbert space ${\mathscr H}={\mathscr H(}\Omega)$ over some (non-empty) set is defined by $\widetilde{A}(\lambda)=\langle…