On a matrix limit theorem†
Tosio Kato · Linear and Multilinear Algebra · 1975
It was shown by Ellis and pinsky [1] that exist with R+ = R− if T and A are m × m matrices with Tskew-hermitian. In the present note we shall try to generalize their result to linear operators in an infinite-dimensional space X As a special case, it turns out that the result is true if X is a Hilbert space. Tis skew-adjoint (not necessarily bounded), and A is compact. In more general casesR± may exist without being equal to each other.