On norm-attainable operators in Banach spaces (Q780088)

The author claims to present new results on norm-attaining operators and functionals. The paper is a collection of statements that look like mathematical results but are mostly written in an unclear way with an arbitrary use of terminology which does not permit to understand their meaning. Say, expressions like ``Let \(H\) be a reflexive, dense, separable, infinite dimensional complex Hilbert space'', or ``We regard \(H^*\) the dual space of a Hilbert space \(H\) to be nonzero throughout this section unless otherwise stated'' make me feel uneasy. A~pleasant exception is Theorem 24 which states that every compact self-adjoint operator on a Hilbert space attains its norm: at least this result is understandable, true, and well-known, so the wording ``dense Hilbert space'' in its statement could be forgiven.