Abstract
In Hardy (Proc Camb Philos 19:86–95, 1916), Hardy defined the normed spaces $$\mathcal {C}_{r}$$ and $$\mathcal {C}_{r0}$$ of all regularly convergent and regularly null double sequences and made convergence factor calculations (i.e. some beta-dual calculations). In this paper, we extend these spaces to the paranormed spaces $$\mathcal {C}_{r}(t)$$ and $$\mathcal {C}_{r0}(t)$$ . Also, we define the paranormed spaces $$\mathcal {C}_{tr}(t)$$ and $$\mathcal {C}_{tr0}(t)$$ of all totally regularly convergent and totally regularly null double sequences. We examine some topological properties of these spaces and determine their alpha-, beta- and gamma-duals.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
