BANACH空间中SCHAUDER框架的若干性质

†. Jhavilalghimire, And Narayan, Prasad Pahari, Sumit Kumar
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引用次数: 0

摘要

定义并研究了满足性质(I)和性质(II)的Schauder框架。已经证明了原子分解满足性质(I)当且仅当它满足性质(II)。此外,定义了满足性质(M)的Schauder框架,并证明了在一致凸Banach空间中,如果Schauder帧满足性质(M),那么它也满足性质(II)(从而满足性质(I))。此外,我们定义了满足性质(B)的原子分解,并证明了性质(B是原子分解满足性质(I)的必要条件。最后,我们定义了Schauder框架的性质(SB),并给出了它的必要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
CERTAIN PROPERTIES ASSOCIATED WITH SCHAUDER FRAMES IN BANACH SPACES
. Schauder frames satisfying property (I) and property (II) has been defined and studied. It has been proved that an atomic decomposition satisfies property (I) if and only if it satisfies property (II). Also, Schauder frames satisfying property ( M ) has been defined and it has been proved that, in a uniformly convex Banach space, if a Schauder frame satisfies property ( M ) , then it also satisfies property (II) (and hence property (I)). Further, we define atomic decompositions satisfying property ( B ) and prove that property ( B ) is a necessary condition for an atomic decomposition satisfying property (I). Finally, we define property ( SB ) for a Schauder frame and gave a necessary condition for it.
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来源期刊
Poincare Journal of Analysis and Applications
Poincare Journal of Analysis and Applications Mathematics-Applied Mathematics
CiteScore
0.60
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