Two paranormal and the set of all entire Drichlet series
Deepanjan Bhattacharya, Susil Kumar Manna · Revista de la Academia Canaria de Ciencias: = Folia Canariensis Academiae Scientiarum · 1999
In this paper, the notion of two-paranorm is introduced, and it is shown that the set of all entire Dirichlet series with different exponents possesses such two-paranorm structure. Next, the concept of Saks space of a two-paranorm space is introduced, and it is proved that the aforesaid two-paranorm space possesses a Saks space. Further, the importance of this Saks space is highlighted in the form of an interesting proposition. Lastly, the definition of a two-paranormed algebra is given and the existence of different types of two-paraalgebraic structures on n is investigated under suitable compositions and paranorms.