New examples of weakly compact approximation in Banach spaces.
Non-containment of l1 in projective tensor products of Banach spaces.
Two properties on projective tensor products are introduced and briefly studied. We apply them to give sufficient conditions to assure the non-containment of l1 in a projective tensor product of Banach spaces.
Norm attaining and numerical radius attaining operators.
In this note we discuss some results on numerical radius attaining operators paralleling earlier results on norm attaining operators. For arbitrary Banach spaces X and Y, the set of (bounded, linear) operators from X to Y whose adjoints attain their norms is norm-dense in the space of all operators. This theorem, due to W. Zizler, improves an earlier result by J. Lindenstrauss on the denseness of operators whose second adjoints attain their norms, and is also related to a recent result by C. Stegall...
Norm attaining bilinear forms on .
Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces
For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.
Norm attaining operators versus bilinear forms.
The well known Bishop-Phelps Theorem asserts that the set of norm attaining linear forms on a Banach space is dense in the dual space [3]. This note is an outline of recent results by Y. S. Choi [5] and C. Finet and the author [7], which clarify the relation between two different ways of extending this theorem.
Numerical radius attaining operators.