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1 引 言 近年来,范数在矩阵计算[2]、扰动理论[4]等领域中的应用越来越广泛.有关范数不等式的运用在一些证明中也越来越常见. 在文[3]中,Horn和Johnson引用了这样的一个范数定理: 命题 V为域F(C或R)上的向量空间,若‖·‖a1,…,‖·‖am为V上的向量范数,‖·‖β是Rm上的向量范数,则函数f:V|→R  相似文献
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LetA e be the algebra obtained by adjoining identity to a non-unital Banach algebra (A, ∥ · ∥). Unlike the case for aC*-norm on a Banach *-algebra,A e admits exactly one uniform norm (not necessarily complete) if so doesA. This is used to show that the spectral extension property carries over fromA to A e . Norms onA e that extend the given complete norm ∥ · ∥ onA are investigated. The operator seminorm ∥ · ∥op onA e defined by ∥ · ∥ is a norm (resp. a complete norm) iffA has trivial left annihilator (resp. ∥ · ∥op restricted toA is equivalent to ∥ · ∥).  相似文献
3.
在本文中,我们证明下述主要结果:并简化了文献[1]中的有关结果  相似文献
4.
In this paper, we show the existence of the strong solutions for the coupled suspension bridge equations. Furthermore, existence of the strong global attractors is investigated using a new semigroup scheme. Since the solutions of the coupled equation have no higher regularity and the semigroup associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.  相似文献
5.
A characterization of Banach spaces admitting uniformly Gâteaux smooth norms in terms of σ-finite dual dentability indices is given. Some applications in the area of weak compactness are discussed. We also study σ-locally uniformly rotund dual renormings in connection with σ-countable dual dentability indices.  相似文献
6.
It is proved that a weighted Orlicz sequence space ?M(w), equipped with Luxemburg or Amemiya norm has weak uniform normal structure iff ?M(w)≅hM(w) for wide class of weight sequences . An example is constructed, where M has not Δ2-condition but by choosing a suitable weight sequence limn→∞wn=∞ we get that ?M(w) has weak uniform normal structure.  相似文献
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