On the complemented subspaces of the Schreier spaces

It is shown that the Schreier space X admits a set of continuum cardinality whose elements are mutually incomparable complemented subspaces spanned by subsequences of the natural Schauder basis of X.Comment: 26 pages, AMS-LaTe

More (\ell_r) saturated (\mathcal{L}_\infty) spaces

We present some new examples of separable (\mathcal_\infty) spaces which are (\ell_r) saturated for some (1 < r < \infty)

On a problem of H.P. Rosenthal concerning operators on C[0,1]

AbstractA problem of H.P. Rosenthal asks whether every bounded linear operator T:C[0,1]→C[0,1] which is an isomorphism on a closed linear infinite-dimensional subspace X not containing any isomorph of c0, is actually an isomorphism on a subspace isomorphic to C[0,1]. An affirmative answer to this problem is provided when T is a contraction whose restriction to X is an isometry

A continuum of totally incomparable hereditarily indecomposable Banach spaces

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On the compact operators case of the Bishop-Phelps-Bollobás property for numerical radius

The authors would like to thank Bill Johnson for kindly answering several inquiries.We study the Bishop–Phelps–Bollobás property for numerical radius restricted to the case of compact operators (BPBp-nu for compact operators in short). We show that C0(L) spaces have the BPBp-nu for compact operators for every Hausdorff topological locally compact space L. To this end, on the one hand, we provide some techniques allowing to pass the BPBp-nu for compact operators from subspaces to the whole space and, on the other hand, we prove some strong approximation property of C0(L) spaces and their duals. Besides, we also show that real Hilbert spaces and isometric preduals of ℓ1 have the BPBp-nu for compact operators

NEW EXAMPLES OF c0-SATURATED BANACH SPACES

For every p ∈ (1, ∞), an isomorphically polyhedral Banach space Ep is constructed which has an unconditional basis and does not embed isomorphically into a C(K) space for any countable and compact metric space K. Moreover, Ep admits a quotient isomorphic to ℓp