关于算子奇异值与算子范数不等式

Some inequalities on the singular values and norms of operators

利用算子分解理论、函数的凸性和单调性,研究了紧算子奇异值的性质,建立了关于紧算子的一类qusi-范数不等式及范数不等式.而且重新证明了一类典型的Clarkson不等式,即如果A,B∈K(H)是正算子,则有当1≤p<∞时,

Using the theory of operator decomposition, the monotonity and convexity of function, some properties of singular values of compact operators are studied in this paper, a class of qusi-norm inequalities and norm inequalities are established. In addition, a remarkable class of Clarkson inequalities are proved again： if A,B∈K（yp） are positive operators, then when 1 ≤ p 〈 ∞,2^1-p｜｜A＋B｜｜p^p≤｜｜A｜｜p^p＋｜｜B｜｜p^p≤｜｜A＋B｜｜p^p;When 0 〈 p ≤ 1 , the inequality is reversed.