On the Bicomplex Gleason–Kahane–Żelazko Theorem
On the Bicomplex Gleason–Kahane–Żelazko Theorem
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关于双复形 Gleason–Kahane–Żelazko 定理
DOI：
10.1007/s11785-015-0455-x
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发表时间：
2016
影响因子：
0.8
通讯作者：
M. Shapiro
中科院分区：
文献类型：
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作者：
M. E. Luna;C. O. Pérez;M. Shapiro
我们证明了双复线性泛函作用于双复Banach代数（具有双曲值范数），使得可逆元素转化为可逆双复数，实际上是乘法泛函，因此是代数同态。我们对此给出两个证明。其中第一个是基于理论的双复全纯函数，我们在这里提出了一些以前没有公布的事实;第二个使用其复杂的前件（经典的格里森-Kahane-Playazko定理）。
We prove that a bicomplex linear functional acting on a bicomplex Banach algebra (with a hyperbolic-valued norm) in such a way that invertible elements are transformed into invertible bicomplex numbers is, in fact, a multiplicative functional and thus, an algebra homomorphism. We give two proofs of this. The first of them is based on the theory of bicomplex holomorphic functions and we present here a number of previously not published facts; the second uses its complex antecedent (classic Gleason–Kahane–Żelazko theorem).