Products Of EP Operators On Hilbert C*-Modules

extend numerical radius for adjointable operators on Hilbert C^* -modules

In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.

*-frames for operators on Hilbert modules

$K$-frames which are generalization of frames on Hilbert spaces‎, ‎were introduced‎ ‎to study atomic systems with respect to a bounded linear operator‎. ‎In this paper‎, ‎$*$-$K$-frames on Hilbert $C^*$-modules‎, ‎as a generalization of $K$-frames‎, ‎are introduced and some of their properties are obtained‎. ‎Then some relations‎ ‎between $*$-$K$-frames and $*$-atomic systems with respect to a...

Regular Operators on Hilbert C * -modules

A regular operator T on a Hilbert C *-module is defined just like a closed operator on a Hilbert space, with the extra condition that the range of (I + T * T) is dense. Semiregular operators are a slightly larger class of operators that may not have this property. It is shown that, like in the case of regular operators, one can, without any loss in generality, restrict oneself to semiregular op...

The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules

Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...

Dynamical Systems on Hilbert C*-Modules

Variational inequalities on Hilbert $C^*$-modules

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory  on  Hilbert $C^*$-modules is studied.