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Perturbations of determinants of nuclear operators in a Hilbert space
Quaestiones Mathematicae ( IF 0.7 ) Pub Date : 2020-07-13 , DOI: 10.2989/16073606.2020.1747565 Michael Gil’ 1
中文翻译:
希尔伯特空间中核算子行列式的扰动
更新日期:2020-07-13
Quaestiones Mathematicae ( IF 0.7 ) Pub Date : 2020-07-13 , DOI: 10.2989/16073606.2020.1747565 Michael Gil’ 1
Affiliation
Abstract
Let be a complex separable Hilbert space with the unit operator I and {dk} be an orthonormal basis in . Let A, Ã be linear operators in , satisfying the conditions . It is proved that the determinants satisfy the inequalities
. These inequalities refine the well-known ones and enable us to establish upper and lower bounds for the determinants of infinite matrices which are “close” to triangular matrices.
中文翻译:
希尔伯特空间中核算子行列式的扰动
摘要
设是一个复数可分希尔伯特空间,单位算符I和 { d k } 是 中的正交基。令A , Ã为线性运算符,满足条件。证明行列式满足不等式
. 这些不等式改进了众所周知的不等式,使我们能够为“接近”三角矩阵的无限矩阵的行列式建立上下界。