On the algebra range of an operator on a Hilbert 𝐶*-module over compact operators

Rajić, Rajna

doi:10.1090/S0002-9939-03-07130-2

On the algebra range of an operator on a Hilbert $C^*$-module over compact operators
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Proc. Amer. Math. Soc. 131 (2003), 3043-3051 Request permission

Abstract:

Let $X$ be a Hilbert $C^*$-module over the $C^*$-algebra $K(H)$ of all compact operators on a complex Hilbert space $H$. Given an orthogonal projection $p \in K(H)$, we describe the set $V^n(A) = \{\langle Ax,x\rangle : x\in X, \langle x,x \rangle =p\}$ for an arbitrary adjointable operator $A\in B(X)$. The relationship between the set $V^n(A)$ and the matricial range of $A$ is established.

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