Solution of normally solvable operator equations in a Hilbert space

Minimax principles for the solution of semilinear gradient operator equations in hilbert space.

A new variational characterization of solutions for an important class of nonlinear operator equations is obtained. The result obtained is used to derive sharp necessary and sufficient conditions for the solvability of such operator equations. Examples of the applicability of the results obtained to nonlinear Dirichlet problems and global differential geometry are discussed.

The solutions to some operator equations in Hilbert $C^*$-module

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 $TXS^*-SX^*T^*= A$.

Operator Preconditioning in Hilbert Space

2010 1 Introduction The numerical solution of linear elliptic partial differential equations consists of two main steps: discretization and iteration, where generally some conjugate gradient method is used for solving the finite element discretization of the problem. However, when for elliptic problems the dis-cretization parameter tends to zero, the required number of iterations for a prescrib...

Operator Extensions on Hilbert Space

the solutions to some operator equations in hilbert c*-module

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.