Geodesic
Proximity and similarity of operators II
Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 205-213

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we continue the examination of the question of similarity of operators A and B begun in reference [3]. In that article, a similarity result was obtained based on a measure of closeness, or proximity, of the uniformly continuous semigroups etA and etB, t>0. The operators considered were elements of B(H), the algebra of bounded operators on a Hilbert space BWe now wish to relax this requirement and replace B(H) by a complex Banach algebra B with unit I. In Section 2 we give a necessary condition for the similarity of A, B ∈ H. We then give a condition sufficient to guarantee A and B are approximately similar (as defined in reference [5]). In Section 3 we restrict our attention to the case where H = H(H). There we give a condition which guarantees A, B ∈ H(H) are intertwined by a Fredholm operator. This leads naturally into a discussion of proximity-similarity in the Calkin algebra si. This is the subject of Section 4. Following reference [7] we define a metric p on N(H), the normal elements of H We show (N(H), p) is a complete metric space and that the unitary orbit of H (N(H) p)is the p-connected component of a in N (H). 
Burnap, Charles; Lambert, Alan. Proximity and similarity of operators II. Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 205-213. doi: 10.1017/S001708950000923X
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