On the Generalization of the Volterra Principle of Inversion.
Interim technical rept.,
MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB
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In the article a linear operator, K, defined on a Hilbert space equipped with a chain of orthoprojectors is considered. It is proved that if K enjoys a particular property with respect to the chain of orthoprojectors, then the series the summation from n0 to infinity of K sup n converges in the uniform operator norm. The proof uses purely algebraic techniques and does not require compactness of K. As such it is a significant generalization of the wellknown Volterra principle of inversion. Author
- Theoretical Mathematics