The boundedness of the set of infinite matrix transformations from convergence-free space to sequence spaces is studied,and a general form of it is deducted.

Let λ and μ be sequence space and have both the signed-weak gliding hump property,(λ,μ) be the algebra of the infinite matrix operators which transform λ to μ.

This paper introduces the research development of the important effect algebra in quantum mechanics,and points out that it is of great significance to the establishment of mathematical foundation of quantum mechanics by making use of infinite matrix theory to study its convergent theory and invariants.

We discuss derivation on infinite matrix rings, and prove that every derivation ofinfinite matrix rings with a finite number of nonzcro entries on a ring R can be represented asthe sum of two special derivations.

Using Antosik-Mikusinski basic matrix theorem? and the subset family, for a type of mapping matrix, a series of matrix transformation theorems is obtained, and the characterizations of a class of infinite matrix transformations is also derived.

The decisive breakthrough in research of infinite matrix transformation is that the action of continuous linear operators in Banach Space on vector sequence, which was started at 1950 by A.

From the Antosik-Mikusinski basic matrix theorem and the subset family,for a type of mapping matrix,an infinite matrix convergence theorem is obtained,and the stronger characterizations of a class of classical infinite matrix transformations were also derived.