The operator equation T(H1nT)n=K
The operator equation T(H1nT)n=K
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DOI：
10.1016/0024-3795(88)90205-4
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发表时间：
1988-10
影响因子：
1.1
通讯作者：
T. Furuta
中科院分区：
文献类型：
--
作者：
T. Furuta
设H和K是Hilbert空间上的有界正算子，且H是非奇异的.证明了若存在正算子T使得对某个自然数n，T（H1nT）n= K，则对任意的自然数m，m ∈ n，存在正算子T1使得T1（H1mT1）m= K.在每种情况下，最多分别有一个正解T和T1.
Let H and K be bounded positive operators on a Hilbert space, and assume that H is nonsingular. This paper shows that if there exists a positive operator T such that T (H 1 n T) n= K for some natural number n, then, for any natural number m such that m⩽ n there exists a positive operator T 1 such that T 1 (H 1 m T 1) m= K. In each case, there is at most one positive solution T and T 1 respectively.