where the best possible constant Mk is it for k ^ 1/2 and ir\ csc irk\ for 1/2 <k. Thus, when considered as a linear operator on the complex sequential Hilbert space l2, Hk is a bounded symmetric operator. Magnus [8] showed that the l2 spectrum of H0 is purely continuous and consists of the interval [0, it]. In this note we shall exhibit for each real k a monotone function pk(\) and an isometri...

In this   paper,  we   present  some  refinements  of the   famous Young  type  inequality.   As  application  of   our   result, we  obtain  some  matrix inequalities   for   the  Hilbert-Schmidt norm  and   the  trace   norm. The results    obtained   in  this  paper  can  be   viewed   as  refinement  of  the   derived  results   by  H.  Kai  [Young  type  inequalities  for matrices,  J.  Ea...

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

in this paper, we state some results on product of operators with closed rangesand we solve the operator equation txs*- sx*t*= a in the general setting of theadjointable operators between hilbert c*-modules, when ts = 1. furthermore, by usingsome block operator matrix techniques, we nd explicit solution of the operator equationtxs*- sx*t*= a.

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its denes a boundedoperator.

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

We examine condition numbers, preconditioners, and iterative methods for finite element discretizations of coercive PDEs in the context of the fundamental solvability result, the Lax-Milgram Lemma. Working in this Hilbert space context is justified because finite element operators are restrictions of infinite-dimensional Hilbert space operators to finite-dimensional subspaces. Moreover, useful ...

in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...