The classical Bohr inequality states that for complex numbers a, b and real numbers p, q > 1 such that 1/p 4- 1/q = 1, we have |a + b~2 ≤ p|a|~2 + q~2 with equality if and only if b = (p - l)a. Various generalizations of the Bohr inequality occur for scalars, vectors, matrices and operators. In this paper, this inequality is generalized from Hilbert space operators to the context of C*-algebras and some extensions and related inequalities are obtained. For each inequality, the necessary and sufficient condition for the equality is also determined. The idea of transforming problems in operator theory to problems in matrix theory, which are easy to handle, plays a key role.
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机译:经典的玻尔不等式指出,对于复数a,b和实数p,q> 1,使得1 / p4-1 / q = 1,我们有| a + b 〜2≤p | a |〜2 +当且仅当b =(p-l)a时q b 〜2相等。标量,向量,矩阵和运算符会发生Bohr不等式的各种概括。本文将这种不等式从希尔伯特空间算子推广到C *代数的上下文,并得到了一些扩展和相关的不等式。对于每个不平等,还确定了平等的必要和充分条件。将运算符理论中的问题转换为矩阵论中的问题(易于处理)的想法起着关键作用。
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