赋准范空间上可加算子族的一致有界性的一个注记

A note of the Uniform Boundedness of Additive Operator Family in Quasi-normed Space

在第二纲的赋准范空间上,证明了可加算子族在拟有界集上的一致有界性.在不受局部拟有界条件限制下,把赋准范空间上可加算子族的一致有界性原理进一步推广,使其应用范围得到扩展.

<Abstrcat> The uniform boundedness of additive operator family is proved on psuedo-bounded set of the second category quasi-normed space . Uniform boundedness principle of additive operator family is expanded on quasi-normed space of evading the straitening conditions of 'local psuedo-boundedness'. Thus, the uniform boundedness principle will be applied to a widened scope.