$n\times n$算子矩阵符号固定的条件
Conditions of fixed sign for $n\times n$ operator matrices
摘要：
得到了作用在任意多个实可分希尔伯特空间乘积上的自伴连续算子矩阵的一个正定性判据，并在附加条件下得到了一个非负性判据.作为应用，讨论了多元Hilbert泛函极值的充分必要条件。
英文摘要：
A positive definiteness criterion and, under the additional conditions, a nonnegativity criterion for a self-adjoint continuous operator matrix, acting in product of an arbitrary number of real separable Hilbert spaces, are obtained. As application, both sufficient and necessary analytical conditions of functional extremum of several Hilbert variables are considered.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
