Boundedness Of The Set Of Infinite Matrix Transformations About Convergence-Free Space

Today, sequence spaces theory is an independed branch of function analysis.The earliest research about sequence spaces theory is D.Hilbert′s paper that square can make sum sequence space l₂. After that, some research have been done about sequence spaces l_p(1≤p<∞),l_∞,c. . These sequence spaces are all detail.In 1934, G. and O.Toeplitz first studied prefect sequence space. Prefect sequence space is a kind of ordinary sequence space. It obtains many sequence spaces which have been studied, but it can not obtains all sequence spaces . For example, it obtains sequence spaces l_p(1≤p<∞),l_∞, but it can not obtains sequence spaces c. After that, other people also studied ordinary sequence space. The work of G. Kothe creat sequence space theory.Infinite matrix transformations can map a sequence space to other sequence space. We obtain the characterizations for the boundedness of the set of infinite matrix transformations from convergence-free space to sequence spaces l_p(1≤p≤∞),c and c₀. Especially,we get the general forms of infinite matrix transformations from convergence-free space to sequence spaces l_p(1≤p≤∞),c₀.