Irreducible Operators and Spectral Pictures
蒋春澜, 续辉 · Chinese Science Bulletin · 1994
A (bounded finear) operator T on a (separable, infinite, dimensional, complex) Hilbert space (?) is said to be irreducible if there is no nontrivial (orthogonal) projection P commuting with T. In Ref. [1], Halmos proved that the set of all irreducible operators is dense in (?)((?)), the algebra of all bounded operators on (?). Gilfeather proved that every normal operator without eigenvalue is similar to an irreducible operator.