Operator-valued Fourier–Haar multipliers on vector-valued $${L^1}$$ spaces II: a characterisation of finite dimensionality
Operator-valued Fourier–Haar multipliers on vector-valued $${L^1}$$ spaces II: a characterisation of finite dimensionality
复制标题
向量值 $${L^1}$$ 空间上的算子值傅立叶-哈尔乘子 II：有限维的表征
DOI：
10.1007/s11117-020-00797-z
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发表时间：
2020
期刊：
影响因子：
1
通讯作者：
H. Wark
中科院分区：
文献类型：
--
作者：
H. Wark
给出了一个充分必要条件，保证了Fourier-Haar乘子算子的有界性
$$L^1（[0，1]，X）$$
到
$$L^1（[0，1]，Y）$$
其中X是任意有限维Banach空间，Y是任意Banach空间. Fourier-Haar乘子序列不是来自
$${\mathbb {R}}$$
与经典情形一样，但从Banach空间X到Banach空间Y的有界算子空间。此外，它表明，该条件的特点是有限维的Banach空间X。
A necessary and sufficient condition is given to ensure the boundedness of Fourier–Haar multiplier operators from
$$L^1 ([0, 1], X)$$
to
$$L^1 ([0, 1], Y)$$
, where X is an arbitrary finite dimensional Banach space and Y is an arbitrary Banach space. The Fourier–Haar multiplier sequences come not from
$${\mathbb {R}}$$
, as in the classical case, but from the space of bounded operators from the Banach space X to the Banach space Y. Moreover, it is shown that this condition characterises the finite dimensionality of the Banach space X.