Regular Operators on Hilbert C * -modules
نویسنده
چکیده
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 operators on C *-algebras. We then prove that for abelian C *-algebras as well as for subalgebras of the algebra of compact operators, any closed semiregular operator is automatically regular. We also determine how a regular operator and its extensions (and restrictions) are related. Finally, using these results, we give a criterion for a semiregular operator on a liminal C *-algebra to have a regular extension.
منابع مشابه
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.
متن کاملSome Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras
In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...
متن کاملProducts Of EP Operators On Hilbert C*-Modules
In this paper, the special attention is given to the product of two modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented that imply the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved that $P(RPQ)$ is idempotent, if $RPQ$†</...
متن کامل*-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...
متن کاملG-frames in Hilbert Modules Over Pro-C*-algebras
G-frames are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*-Hilbert modules. In this paper, we first generalize the concept of g-frames to Hilbert modules over pro-C*-algebras. Then, we introduce the g-frame operators in such spaces and show that they sha...
متن کامل