A surprising number of managers suffer from imposter syndrome. How to get rid of it?

Imposter syndrome is a phenomenon that affects many people but is very common among managers, and especially those who have only recently reached their current post or not long ago been promoted from a regular position. They have a constant feeling of not being good enough for the job, that their promotion was a mistake and it may become apparent at any moment that they simply are not up to the task. So how should one combat imposter syndrome?