Harmonic Analysis of Operators on Hilbert Space

Bela Sz.-Nagy

Ciprian Foias

North-Holland Publishing

Theory Of Generalized Spectral Operators (Mathematics and Its Applications)

Science & Math

Ion Colojoara

Mathematics

Gordon & Breach

Béla Szőkefalvi-Nagy

Hari Bercovici

László Kérchy

North-Holland

<p>Classical H~ interpolation theory was conceived at the beginning of the century by C. Caratheodory, L. Fejer and I. Schur. The basic method, due to Schur, in solving these problems consists in applying the Mobius transform to peel off the data. In 1967, D. Sarason encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, B. Sz.- Nagy and C. Foias obtained a purely geometrical extension of Sarason's results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries; starring with R. G. Douglas, P. S. Muhly and C. Pearcy, this is referred to as the commutant lifting theorem. In 1957, Z. Nehari considered an L ~ interpolation problern which in turn encompassed the same classical interpolation problems, as well as the computation of the distance of a function f in L ~ to H~. At about the sametime as Sarason's work, V. M.</p>

The Commutant Lifting Approach to Interpolation Problems (Operator Theory: Advances and Applications)

Arthur E. Frazho

History & Philosophy

Birkhauser

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