This paper presents a survey of most of the known fundamental results
involving the sequence spaces l(p), c0(p), c(p) and l?(p), w0(p), w(p) and
w?(p), f0(p) and f (p). These spaces are generalizations of the classical BK
spaces lp, c0, c and l?, the spaces wp 0, wp and wp? of sequences that are
strongly summable to zero, strongly summable and strongly bounded with index
p by the Ces?ro method of order 1, and of almost null and almost convergent
sequences, respectively. The results inlude the basic topological properties
of the generalized spaces, the complete lists of their known ?-, ?-, ?-,
functional and continuous duals, and the characterizations of many classes
of matrix transformations between them, in particular, the complete list of
characterizations of matrix transformations between the spaces l(p), c0(p),
c(p) and l?(p). Furthermore, a great number of interesting special cases are
included. The presented results cover a period of four decades. They are
intended to inspire the inreasing number of researchers working in related
topics, and to provide them with a comprehensive collection of results they
may find useful for their work.