2 problems

Three-type existence claim. Every infinite-dimensional Banach space $\mathfrak X$ admits a bounded biorthogonal system $\left\{x_n,x_n^*\right\}$ that is one of the following three…

Let $\mathcal H$ be the Hilbert space under consideration, and let $\mathcal F_{\hat e}=\{\hat e_n\}$ be the orthonormal set obtained from the positive square roots of the operator…