## Dodzi Attimu, Toka Diagana

*Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces *

Comment.Math.Univ.Carolin. 50,1 (2009) 37-60. **Abstract:**This paper is mainly concerned with extensions of the so-called Vishik functional calculus for analytic bounded linear operators to a class of unbounded linear operators on $c_0$. For that, our first task consists of introducing a new class of linear operators denoted $W(c_0({J},\omega ,\Bbb K))$ and next we make extensive use of such a new class along with the concept of convergence in the sense of resolvents to construct a functional calculus for a large class of unbounded linear operators.

**Keywords:** non-archimedean Banach space, Shnirelman integral, spectrum, unbounded linear operator, functional calculus

**AMS Subject Classification:** Primary 47S10, 46S10; Secondary 12G25, 26E30