Die Nuklearität der Ultradistributionsräume und der Satz vom Kern I.
In the present paper we introduce some double sequence spaces defined by a sequence of modulus function over -normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces.
In this paper, we define some classes of double sequences over -normed spaces by means of an Orlicz function. We study some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined.
In this note we study three operators which are canonically associated with a given linear and continuous operator between locally convex spaces. These operators are defined using the spaces of bounded sequences and null sequences. We investigate the relation between them and the original operator concerning properties, like being surjective or a homomorphism.