The Commutant Lifting Approach to Interpolation Problems: v. 44 (Operator Theory: Advances and Applications) - Hardcover

Foias, Ciprian; Frazho, A. E.

Hardcover

ISBN 10: 3764324619 ISBN 13: 9783764324612

Publisher: Birkhauser Verlag AG, 1990

Synopsis

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.

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 1990
• ISBN 10: 3764324619
• ISBN 13: 9783764324612
• Binding: Hardcover
• Language: English
• Number of pages: 632