Equivalence of Bases in Non-archimedean Banach Spaces
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 . For that, our first task consists of introducing a new class of linear operators denoted 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.
By means of two general operations + and x, called pan-operations'', we build a new kind of integral. This formulation contains, as particular cases, both Choquet's and Sugeno's integrals.