Conditions for eigenvectors of a selfadjoint operator-function to form a basis |
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Authors: | Vladimir Matsaev Efim Spigel |
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Institution: | (1) School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel;(2) Technological Institute, Holon, Israel |
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Abstract: | Consider a functionL() defined on an interval of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point 0 and a vector
0 H(
0 0) are called eigenvalue and eigenvector ofL() ifL() ifL(0)
0 = 0. Supposing that the functionL() can be represented as an absolutely convergent Fourier integral, the interval is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL() corresponding to the eigenvalues from the interval form an unconditional basis in the subspace spanned by them. |
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Keywords: | Primary 47A56 Secondary: 47A75 |
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