## Generalized involutions on Banach spaces.(English)Zbl 1052.47029

The purpose of this paper is to study the class of bounded linear operators $$T$$ on a complex Banach space such that $$T^m= I$$ for some positive integer $$m$$. It is well-known that such an operator is scalar-type spectral, from which all the results of the paper easily follow.

### MSC:

 47B40 Spectral operators, decomposable operators, well-bounded operators, etc. 47A60 Functional calculus for linear operators 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)