Correction to: A Class of Hereditarily l p Banach Spaces Without Schur Property

A Class of Hereditarily $ell_p(c_0)$ Banach spaces

We extend the class of Banach sequence spaces constructed by Ledari, as presented in ''A class of hereditarily $ell_1$ Banach spaces without Schur property'' and obtain a new class of hereditarily $ell_p(c_0)$ Banach spaces for $1leq p<infty$. Some other properties of this spaces are studied.

Interpolating Hereditarily Indecomposable Banach Spaces

A Banach space X is said to be Hereditarily Indecomposable (H.I.) if for any pair of closed subspaces Y , Z of X with Y ∩ Z = {0}, Y + Z is not a closed subspace. (Throughout this section by the term “subspace” we mean a closed infinite-dimensional subspace of X .) The H.I. spaces form a new and, as we believe, fundamental class of Banach spaces. The celebrated example of a Banach space with no...

A New Class of Banach Sequence Spaces

a new class of banach sequence spaces

0

Strictly Singular Non-compact Operators on Hereditarily Indecomposable Banach Spaces

An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic `1 Banach space. The construction of this operator relies on the existence of transfinite c0-spreading models in the dual of the space.