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The parallel sum for adjoinable operators on Hilbert $C^*$-modules is introduced and studied. Some results known for matrices and bounded linear operators on Hilbert spaces are generalized to the case of adjointable operators on Hilbert $C^*$-modules. It is shown that there exist a Hilbert $C^*$-module $H$ and two positive operators $A, Binmathcal{L}(H)$ such that the operator equation $A^{1/2}=(A+B)^{1/2}X, Xin cal{L}(H)$ has no solution, where $mathcal{L}(H)$ denotes the set of all adjointable operators on $H$.
We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner product struct
The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras th
We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea of geomet
Let $A$ be a $C^*$-algebra. Let $E$ and $F$ be Hilbert $A$-modules with $E$ being full. Suppose that $theta : Eto F$ is a linear map preserving orthogonality, i.e., $<theta(x), theta(y) > = 0$ whenever $<x, y > = 0$. We show in this article that if,
We prove that an arbitrary (not necessarily countably generated) Hilbert $G$-$cla$ module on a G-C^* algebra $cla$ admits an equivariant embedding into a trivial $G-cla$ module, provided G is a compact Lie group and its action on $cla$ is ergodic.