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Keywords:
non-archimedean Banach space; Shnirelman integral; spectrum; unbounded linear operator; functional calculus
non-archimedean Banach space; Shnirelman integral; spectrum; unbounded linear operator; functional calculus
Summary:
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.
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