We develop standard models for commuting tuples of bounded linear operators on a Hilbert space under certain polynomial positivity conditions, generalizing the work of V. Müller and F.-H. Vasilescu in [6], [14]. As a consequence of the model, we prove a von Neumann-type inequality for such tuples. Up to similarity, we obtain the existence of in a certain sense “unitary” dilations.

This manuscript develops the study of reverse Hilbert-type inequalities by applying Hölder on T. We generalize inequality with power two replacing a new β,β>1. The main results are proved using Specht’s ratio, chain rule and Jensen’s inequality. Our (when T=N) essentially new. Symmetrical properties play an essential role in determining correct methods to solve inequalities.

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

X iv :m at h/ 04 06 10 8v 1 [ m at h. FA ] 6 J un 2 00 4 QUADRATIC REVERSES OF THE CONTINUOUS TRIANGLE INEQUALITY FOR BOCHNER INTEGRAL OF VECTOR-VALUED FUNCTIONS IN HILBERT SPACES SEVER S. DRAGOMIR Abstract. Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are prov...

Abstract A more accurate half-discrete Hilbert-type inequality in the whole plane with multi-parameters is established by use of Hermite–Hadamard’s and weight functions. Furthermore, some equivalent forms special types inequalities operator representations as well reverses are considered.

The Hooman{Wielandt inequality which gives a bound for the distance between the spectra of two normal matrices, is generalized to normal operators A; B on a separable Hilbert space, such that A ? B is Hilbert{Schmidt.

In the field of geometric inequalities, the expression Bonnesen type is used after Bonnesen clasical refinement of the isoperimetric inequality (cf., for instance, [Os1], [Os2]), where the deviation from the case of equality (the disc) is given in terms of the outer radius and the inradius of a bounded convex body. The term stability type inequality is also used in a related way (cf. [Gr]), mea...

We study the antieigenvectors of the generalized eigenvalue problem Af = λBf by using the concept of stationary vectors and then obtain an operator inequality complementary to Schwarz’s inequality in Hilbert space. AMS Mathematics Subject Classification (2000): 47A63,47A75