>>16872612
Rotation by 90° around the origin in R^2 has none?

Only if you formulate this problem in apple and banana

Depends on the type of the operator. Compact, normal and subnormal operators have been proven.

>>16872648
Should have said complex Hilbert space. My bad

>>16872612
yes

technically you should not be able to solve this, it is an open question even more the most gifted, 4chan isn't the place for solution to open questions
that aside

finite-dimensional complext hilbert space dim>1, yes
nonseparable hilbert space, yes
many operator classes on hilbert space yes

if hilbert space is real, no in 2+ dims