For a self-adjoint unbounded operator D on a Hilbert space H, a bounded operator y on H and some Borel functions g(t) we establish inequalities of the type [g(D),y]≤ Aoy+A1[D,y]+A2[D,[D,y]]+ +AN[D,[D,...[D,y]...]]The proofs take place in a space of infinite matrices with operator entries, and in this setting it is possible to approximate the matrix associated to [g(D),y] by the Schur product of a matrix approximating [D, y] and a scalar matrix. A classical inequality on the norm of Schur products may then be applied to obtain the results.
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机译：对于Hilbert Space H上的自伴随的无界限运算符D，H和一些BOREL函数G（t）的有界操作员Y和一些BOREL函数G（t）我们建立了类型的不等式 [g（d），y] ≤ao Y + A1 [D，Y] + A2 [D，[D，Y]] + + AN [D，[D，... [[D，Y] .. 。]] 证明在具有操作员条目的无限矩阵的空间中进行，并且在该设置中，可以通过矩阵近似的SCHUR乘积近似于[G（D），Y]相关联的矩阵[D. ，y]和标量矩阵。 然后可以应用Schur产品规范的经典不等式以获得结果。
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