We prove a structure theorem for finite-dimensional indefinite-signature metric 3-Lie algebras admitting a maximally isotropic centre. This algebraic condition indicates that all the negative-norm states in the associated Bagger–Lambert theory can be consistently decoupled from the physical Hilbert space. As an immediate application of the theorem, new examples beyond index 2 are constructed. T...

In this work, we consider the question of local Hilbert space factorization in 2D conformal field theory. Generalizing previous work on entanglement and open-closed TQFT, interpret CFT states terms path integral processes that split join spaces circles intervals. More abstractly, these are cobordisms an extended which defined purely OPE data. addition to usual sewing axioms, impose boundary con...

The Dicke model exhibits a variety of phase transitions. quantum transition from the normal to super-radiant is marked by dramatic change in scaling participation ratio. We find that ground state multifractality manifest ratio as square root full Hilbert space dimension. thermal temperature, for which we obtain an exact analytical expression, strikingly captured mutual information between two s...

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

The BMS (Bondi--van der Burg--Metzner--Sachs) symmetry arises as the asymptotic of flat spacetime at null infinity. In particular, algebra for three-dimensional (${\mathrm{BMS}}_{3}$) is generated by super-rotation generators that form a Virasoro subalgebra with central charge ${c}_{L}$, together mutually commuting super-translation generators. and supertranslation have nontrivial commutation r...

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.

In this paper, we provide a short account of the study of Hilbert-typeinequalities during the past almost 100 years by introducing multi-parametersand using the method of weight coefficients. A basic theorem of Hilbert-typeinequalities with the homogeneous kernel of −−degree and parameters is proved.

In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.