Let A be a bounded linear operator from a couple (X _0, X _1) to a couple (Y _0, Y _1) such that the restrictions of A on the end spaces X _0 and X _1 have bounded inverses defined on Y _0 and Y _1, respectively. We are interested in the problem of how to determine if the restriction of A on the space (X0,X1)θ,q has a bounded inverse defined on the space (Y0,Y1)θ,q. In this paper, we show that a solution to this problem can be given in terms of indices of two subspaces of the kernel of the operator A on the space X _0+X _1.
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机译：设A是从一对（X _0，X _1）到一对（Y _0，Y _1）的有界线性算子，以使A对末端空间X _0和X _1的限制具有在Y _0和X上定义的有界逆。 Y _1。我们对如何确定A对空间（X0，X1）θ，q的限制是否具有在空间（Y0，Y1）θ，q上定义的有界逆数的问题感兴趣。在本文中，我们表明可以通过空间X _0 + X _1上算子A的核的两个子空间的索引来给出该问题的解决方案。
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