Geodesic
Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 37-60.

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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.
Classification : 12G25, 26E30, 46S10, 47S10
Keywords: non-archimedean Banach space; Shnirelman integral; spectrum; unbounded linear operator; functional calculus 
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Attimu, Dodzi; Diagana, Toka. Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 37-60. http://geodesic.mathdoc.fr/item/CMUC_2009__50_1_a3/