230问答网 > 设A,B为Hilbert空间H上的两个线性算子，且<Ax,y>=<x,By>,任意x,y∈H,证明A是有界的。

设A,B为Hilbert空间H上的两个线性算子，且<Ax,y>=<x,By>,任意x,y∈H,证明A是有界的。

2025-03-20 14:50:56
推荐回答（1个）
回答1：

固定||x||=1，令fx(y)=,可以证明它是有界线性泛函，并且还可以知道，此时||Ax||=||fx||，由共鸣定理知道，对于任意x，||A||有界

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