Norm-attaining Lipschitz functionals

Norm Attaining Multilinear Forms on L1(μ)

Given an arbitrary measure μ, this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on L1 μ . However, we have the density if and only if μ is purely atomic. Furthermore, the study presents an example of a Banach space X in which the set of norm attaining operators from X into X∗ is dense in the space of all bounded linea...

Norm aúaining and numerical radius attaining operators

ABSTRAer. In Ihis note we discusa sorne results oit numerical radius altaining operators paralleling carlier results Oit norm attaining operatora. Eorarbitrary Banach spacesXand Y, the set of (bounded, linear) operatora from Xto Ywhose adjoints altain [heir norms is norm-dense ita [hespaee of ah operators. This theorem. due toW. Zizíer, improves an earlier result by J. Lindenstrauss on the dens...

Denseness for norm attaining operator-valued functions

In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss’ famous result on the denseness of norm attaining operators. Specifically, we show given any A ∈ L(H) there is a sequence of rank-1 operators Kn such that A+Kn is norm attaining for each n and Kn converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operato...

A Geometric Estimate on the Norm of Product of Functionals

The open problem of determining the exact value of the n-th linear polarization constant cn of R n has received considerable attention over the past few years. This paper makes a contribution to the subject by providing a new lower bound on the value of sup‖y‖=1 | 〈x1,y〉 · · · 〈xn,y〉 |, where x1, . . . ,xn are unit vectors in R. The new estimate is given in terms of the eigenvalues of the Gram ...

Additive functionals on spaces with non-absolutely-continuous norm