Almost Over Complete and Overtotal Sequences with Almost Square and Subprojectivity of Banach Spaces

Abstract

We provide information about the structure of a sequence in a separable Banach space. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square. We show that every space containing a copy of c_0 can be renormed to be almost square. A local and a weak version of almost square spaces are also studied. We study superprojective Banach spaces. We show that they cannot contain copies of l_(1,)which restricts the search for non-reflexive examples of these spaces. We examine the stability of subprojectivity of Banach spaces under various operations, such as direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces.