Titlebook: Operator Algebras, Operator Theory and Applications; 18th International W J. J. Grobler,L. E. Labuschagne,M. M?ller Conference proceedings

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A Time-variant Norm Constrained Interpolation Problem Arising from Relaxed Commutant Lifting, triangular operator matrices of which the columns induce contractive operators. The set of all solutions of the problem is described explicitly. The results presented are time-variant analogues of the main theorems in [.].

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On an Interpolation Problem for Generalized Schur Functions,tions in a generalized Schur class . for every .≥.. where the integer .. equals the number of negative eigenvalues of the Pick matrix associated to the problem and completely determined by interpolation data. A linear fractional description of all . solutions of the (nondegenerate) problem is well k

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Holomorphic , and Bergman-type Spaces,∞). Further, under mild conditions on the weight function . we characterize lacunary series in . space. Finally, we study the boundedness and compactness of composition operators between . and Bergman spaces.

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A Time-variant Norm Constrained Interpolation Problem Arising from Relaxed Commutant Lifting,general form the problem already appears in the analysis of the set of all solutions to the three chain completion problem. The interpolants are upper triangular operator matrices of which the columns induce contractive operators. The set of all solutions of the problem is described explicitly. The

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