The four block problem is a generalization of Nehari's problem for matrix Functions. It plays an important role in H-infinity-optimal control theory. It is well known that Nehari's problem for a continuous scalar function has a unique solution. However, in the matrix case the situation is quite different. V. V. Peller and N. J, Young (1994, J. Funct. Anal. 120, 300-343) studied superoptimal solutions of Nehari's problem. They minimize not only the L-infinity-norm of the corresponding matrix function but also the essential suprema of all Further singular values. It was shown that for H-infinity+C matrix functions Nehari's problem has a unique super-optimal solution. In this paper we study superoptimal solutions of the four block problem and we find a natural condition under which such a superoptimal solution is unique. Our result is new even in the case of Nehari's problem. We study some related problems such as thematic factorizations, invariance of indices, and inequalities between the singular values of the four block operator and the super optimal singular values. (C) 1997 Academic Press. [References: 24]
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机译：四块问题是矩阵函数的Nehari问题的推广。它在H无限最优控制理论中起着重要作用。众所周知，连续标量函数的Nehari问题具有独特的解决方案。但是，在矩阵情况下情况则大不相同。 V. V. Peller和N. J，Young（1994，J. Funct。Anal。120，300-343）研究了Nehari问题的超最优解。它们不仅最小化了相应矩阵函数的L-无穷范数，而且还最小化了所有进一步奇异值的基本前提。结果表明，对于H-无穷大+ C矩阵函数，Nehari问题具有唯一的超最优解。在本文中，我们研究了四嵌段问题的最优解，并找到了一个自然条件，在这种条件下，最优解是唯一的。即使在内哈里问题的情况下，我们的结果也是新的。我们研究了一些相关问题，例如主题分解，索引不变性以及四块算子的奇异值与超最优奇异值之间的不等式。 （C）1997学术出版社。 [参考：24]
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