We prove that any bijective fidelity preserving transformation on the set of all density operators on a Hilbert space is implemented by an either unitary or antiunitary operator on the underlying Hilbert space. Let H be a Hilbert space. The set of all density operators on H, that is, the set of all positive self-adjoint operators on H with finite trace is denoted by C 1 (H). (We note that one m...

The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U (N + , N −) are provided. They generalize the Virasoro and W ∞ algebras to higher dimensions. The connection with volume-preserving diffeomorphisms on M , higher generalized-spin and tensor operator algebras of U (N + , N −) is discussed. These centrally-extended,...

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(Fr) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q ⊗̄L(Fr), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure preserving action of a free group Fr, 2 ≤ r ≤ ∞, on a probability ...

Applying the fractional Fourier transform and the Wigner distribution on a signal in a cascade fashion is equivalent with a rotation of the time and frequency parameters of the Wigner distribution. This report presents a formula for all unitary operators that are related to energy preserving transformations on the parameters of the Wigner distribution by means of such a cascade of operators. Fu...

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

‎In this paper we study the residual spectrum of the quasi-split unitary group $G=U(n,n)$ defined over a number field $F$‎, ‎coming from the Borel subgroups‎, ‎$L_{dis}^2(G(F)backslash G(Bbb A))_T$‎. ‎Due to lack of information on the local results‎, ‎that is‎, ‎the image of the local intertwining operators of the principal series‎, ‎our results are incomplete‎. ‎However‎, ‎we describe a conjec...

We derive an expression for the fluctuations of energy in open quantum system undergoing a nontrivial evolution. The statistics are constructed by means two-point measurement process when has been evolved completely positive and trace-preserving map. depend only on state dynamical map generating In particular, we consider Tasaki–Crooks fluctuation theorem, where unitary evolution is replaced ch...

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.