In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foiaş, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative commutant lifting theorem. This is used to solve new operator-valued interpolation problems of SchurCarathéodory, Nevanlinna-Pick, and Sarason type on Fock s...

Abstract. There is a family of potentials that minimize the lowest eigenvalue of a Schrödinger eigenvalue under the constraint of a given L norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when the potential is not one of these optimal potentials. Our results are analogous to those for the isoperimetric problem and the Sobolev inequality. We al...

An Ostrowski type inequality for general convex functions defined on linear spaces is generalised. Some inequalities which improve the HermiteHadamard type inequality for convex functions defined on linear spaces are derived using the obtained result. The results in normed linear spaces are used to obtain some inequalities which are related to the given norm and associated semi-inner products, ...

Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to L-minimum norm control problems, L∞norm minimization, and a class of ...

We prove that the Harish-Chandra’s Schwartz space associated with a discrete subgroup of a semisimple Lie group is a dense subalgebra of the reduced C∗-algebra of the discrete subgroup. Then, we prove that the reduced C∗-norm is controlled by the norm of the Harish-Chandra’s Schwartz space. This inequality is weaker than property RD and holds for any discrete group acting isometrically, properl...

We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with mult...

In this paper we consider the following problem: viewing both a nonlinear system model and its linearization as mappings from input-tostate, we define the error between the state of the original nonlinear system and that of the linearization and find the region of the state space where this error is norm-bounded, in the integral-square (or L2-norm) sense. Using the Hamilton–Jacobi inequality we...

Abstract The topic of this work is the discretization of stationary incompressible Navier-Stokes equations in two dimensions by the cell centered finite volume method. The main results of this work are the existence and the uniqueness of the finite volume discrete problem and the convergence of the velocity in the L2 norm and the discrete norm. Our techniques are based on the construction of a ...

This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related comparison holds for any convex function of a random matrix drawn from the Stiefel manifold. For certain norms, a reversed inequality is also valid. Mathematics ...