Norm Attaining Bilinear Forms onL1[0,1]

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...

Bilinear Forms

The geometry of Rn is controlled algebraically by the dot product. We will abstract the dot product on Rn to a bilinear form on a vector space and study algebraic and geometric notions related to bilinear forms (especially the concept of orthogonality in all its manifestations: orthogonal vectors, orthogonal subspaces, and orthogonal bases). Section 1 defines a bilinear form on a vector space a...

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 note on bilinear forms