The corona problem was raised when mathematicians studied the homomorphism of Hinfinity(D) and maximal ideals in 1960's. It has two equivalent formulations. We refer to the following one as the corona problem. If fin i=1⊂Hinfinity (D), when does there exist functions gin i=1⊂Hinfinity (D) such that i=1n figi = 1 in the unit disk?;In 1962, Carleson determined when a finitely generated ideal in Hinfinity(D) is actually all of Hinfinity(D), by giving a function theory condition on the generators. Namely, I(f 1, f2, f3, ..., fn) = Hinfinity( D) if and only if there exists a epsilon > 0, so that i=1nf iz 2>32 for all z ∈ D. Actually, more was shown, as abound for the size of solutions was given. More precisely, if fin i=1⊂Hinfinity (D) such that 1 ≥ i=1nf iz 2>32>0 for all z ∈ D, then there exists a B(epsilon, n) < infinity and gin i=1⊂Hinfinity (D) with i=1n figi = 1 and i=1ngi z&vbm0;2 ≤ B(epsilon, n) for all z ∈ D. Carleson's proof of what has come to be known as the corona theorem was based on an intricate geometrical construction, of combinatorial character. His proof has been improved by the work of T. Wolff, done in the spring of 1979.;In this paper, we extend the vector valued corona theorem on a reproducing kernel Hilbert space to the matrix case. We proved that if the vector valued corona theorem on a reproducing kernel Hilbert space holds, then so does the corresponding matrix version of corona theorem on some algebras of functions on reproducing kernel Hilbert spaces.
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机译：当数学家在1960年代研究Hinfinity（D）的同态和最大理想时，提出了电晕问题。它有两个等效的公式。我们将以下问题称为电晕问题。如果fin i =1⊂Hinfinity（D），何时存在函数gin i =1⊂Hinfinity（D）使得单位圆盘中i = 1n figi = 1 ?; 1962年，Carleson确定了何时有限地产生理想通过为生成器提供函数理论条件，Hinfinity（D）实际上就是Hinfinity（D）的全部。即，当且仅当存在ε> 0时，I（f 1，f2，f3，...，fn）= Hinfinity（D），所以对于所有z∈D，i = 1nf iz 2> 32。实际上，显示了更多，因为给出了解决方案的大小。更准确地说，如果fin i =1⊂Hinfinity（D）使得对于所有z∈D≥1≥i = 1nf iz 2> 32> 0，则存在B（epsilon，n）展开▼
