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Gohberg: A maximum entropy principle for contractive interpol ants, J. Funct Anal 65 ( 1986), 83-125. [M] Moran, M. : On intertwining operators, to appear in J. of t1atIJ. Anal andAppl [N-F] Nagy, B. - and C. Foias: Harmonic analysis of operators on Hilbert spaces, Amsterdam-Budapest, 1970. Rodri~Arocena - Postal address: Jose M. Montero 3006, ap. 503 - Montevideo, URUGUAY Operator Theory: Advances and Applications, Vol. 41 © 1989 Birkhiiuser Verlag Basel 25 FACTORIZATION AND GENERAL PROPERTIES OF NONLINEAR TOEPLITZ OPERATORSl Joseph A.

29) All algebras Aa' a f I min , are mutually algebraically isomorphic. e. e. ww(A)" ~ Zw(A) Under these additional assumptions the non-abe1ianess is implied also for all local algebras w (A )", if GPC is assumed. w a LEMMA 4. Let the five-tuple (I, (A I (29), (31) be satisfied and assume GPC. ww(Aa )" ~ Zw(a) for all a Proof. e. I. f Po w (AQ )" C w (A ~O I' A, i, wI be given. Assume that there is an index a O with w (A ) .. - Zw (a O) . e. w P one According to (29) for each atomic index is algebraically isomorphic to abelian.

Le. card (I min ) may be larger than ~ O. For some purposes a second condi tion is imposed. (8) Every index a ( I is a supremum of a finite set of minimal indices f3 j ( I min • j - 1. • n. • f3 n ). The motivation for introducing the minimal condition is. on the one hand. that of discretization: one claims to consider. for example in the context of a Minkowski space theory. discrete variants of the theory. On the other hand. the concepts to begin with should be sufficiently general to include the often used index set of all finite-dimensional subspaces of a given infinite-dimensional separable Hilbert space.

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