算子T的强有界、有界和连续性问题

The strong boundedness,boundedness, continuous of the operator T

在赋范线性空间中算子T强有界、有界及连续性三者是相互等价的,但对于赋准范线性空间(F-space)而言,强有界一定是有界、连续的,反之不然,但其中有界和连续性是等价的。

In normed liner space, the strong boundedness , boundedness , continuous of the operator T is equivalent, then in F- space , The strong bounded operatou T is also bounded , continuous operator, but the converse is not true.