Operators in vector sequence spaces. (Spanish: Operadores en espacios de sucesiones vectoriales)

Abstract

For an arbitrary sequence of Banach spaces, the space of corresponding vector-valued, p -summable sequences is considered, 1≤p<∞ . Each bounded linear operator from such a space into an arbitrary Banach space is identified by the corresponding coordinate sequence, that is, by the sequence of its restrictions to each summand. Simple criteria for an operator to be compact, weakly compact, Dieudonné, Dunford-Pettis and unconditionally convergent are given in terms of its coordinate sequence. Corresponding Banach space properties defined by the operator ideals mentioned above are reduced to the same properties for each summand.