Almost Chebyshëv subspaces in the spaces of compact operators (Q1921832)

A closed linear subspace \(E\) of a Banach space \(X\) is called almost Chebyshev subspace, if the elements \(x\in X\), for which the set \(P_E=\{y\in E: |x-y|=\inf_{z\in E} |x-z|\}\) consists of one point, are dense in \(X\). The paper deals with the approximation properties of the space \(K(C(T)\), \(C(Q))\) of compact linear operators acting between the spaces of continuous functions \(C(T)\), \(C(Q)\). The author gives a characterization for finite-dimensional almost Chebyshev subspaces of \(K(C(T)\), \(C(Q))\) and establishes a series of properties of these subspaces.