Geodesic
Essentially Convexoid Operators
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 257-274

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

Let H be a separable complex Hilbert space and let B(H) denote the algebra of all bounded linear operators on H. Let π be the quotient mapping from B(H) onto the Calkin algebra B(H)/K(H), where K(H) denotes all compact operators on B(H). An operator T ∈ B(H) is said to be convexoid[14] if the closure of its numerical range W(T) coincides with the convex hull co σ(T) of its spectrum σ(T). T ∈ B(H) is said to be essentially normal, essentially G 1, or essentially convexoid if π(T) is normal, G 1 or convexoid in B(H)/K(H) respectively. 
Furuta, Takayuki. Essentially Convexoid Operators. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 257-274. doi: 10.4153/CJM-1981-021-x
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