On invex programming problem in Hilbert spaces

Equilibrium Programming in Hilbert Spaces

Several methods for solving systems of equilibrium problems in Hilbert spaces – and for finding best approximations thereof – are presented and their convergence properties are established. The proposed methods include proximal-like block-iterative algorithms for general systems, as well as regularization and splitting algorithms for single equilibrium problems. The problem of constructing appr...

Generalized Frames in Hilbert Spaces

FUSION FRAMES IN HILBERT SPACES

Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.  

Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

On the Decomposition of Hilbert Spaces

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...