in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

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, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.

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.

An essential aspect of a generally covariant system is the invariance of its action under reparametrizations; this means that the label that parametrizes the trajectories of the system is not the time but a physically irrelevant parameter. As a consequence, the system is constrained to remain on the hypersurface of the phase space where the Hamiltonian is null. In fact, since the “evolution” ge...

Marginal β deformations of N = 4 super-Yang-Mills theory are known to correspond to a certain class of deformations of the S background subspace of type IIB string theory in AdS5 × S. An analogous set of deformations of the AdS5 subspace is reviewed here. String energy spectra computed in the near-pp-wave limit of these backgrounds match predictions encoded by discrete, asymptotic Bethe equatio...

We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. A...