We study similarity to partial isometries in C*-algebras as well as their relationship with generalized inverses. Most of the results extend some recent results regarding partial isometries on Hilbert spaces. Moreover, we describe partial isometries by means of interpolation polynomials.
Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and (H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {e} of H, a bijection α: (H) → L(H) can be defined. The aim of this paper is to characterize α (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.
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