Hilbert空间就范直交系的完备性

作者给出了Hilbert空间中就范直交系的完备性的一个判决.该判决推进了Birkhoff和Rota的一个类似判决.Birkhoff和Rota的判决需要假设算子是迹类算子.而所给出的判决只需要假设算子是紧算子.Birkhoff和Rota的的证明，经过Tsao简化后，仍然需要较复杂的分析计算，然而Fredholm理论的运用使得本文中的证明完全避免了复杂的计算.

On the completenes of an orthonormal set

A criterion on the completeness of an orthonormal set in a Hilbert space presented. The new criterion which extends Birhoff and Rotas result is in terms of the compactness of an operator on a Hilbert space. Birhoff and Rotas criterion, if restated in the language of operator theory, is assuming the trace class membership of the corresponding operator. The approach presended in this paper, which involves Fredholm theory, avoids all the computations as presented in Birhoff and Rotas original proof and then simplified by Tsao.