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The desired inequality is then derived by applying the technique of interpolation of analytic families of linear operators. We refer the reader to Stein's book [8J for the details of this program. Our purpose here is to show that the estimates for the cases p > 1 and ~e a > 1 can be obtained by transference. that P Y Moreover, we need only assume is a subpositive contraction for each y. Thus, we offer an alternative to the martingale approach we described above that is applicable to a larger class of semigroups.

47 BIQUASITRIANGULAR OPERATORS AND QUASISIMILARITY Carl Pearcy The University of Michigan Ann Arbor, Michigan Ciprian Foia§ and Dan Voiculescu Mathematics Institute Bucharest and The authors consider the question of whether the class (BQT) consisting of all those (bounded) operators on a fixed Hilbert space qs ~ that are quasisimilar to some biquasitriangular operator is equal to the algebra ';tC'H) of all operators on the space. It is shown that (BQT) qs is at least norm-dense in ~(~) . r and let be a separable, infinite-dimensional, complex Hilbert space, ~(~) denote the algebra of all bounded linear operators on Recall that two operators Tl and there exist operators X and dense range such that TIX = XT 2 T2 Y in in ~(}f) and YT I Df(If) }f are quasisimilar if with trivial kernel and T2Y.

Jl) is a positive idempotent contraction. Thus, using this theorem we have: N N I atRtflPc4J. t=o (3) -? Jl The proof we just gave is modeled after a real-line argument of A. P. Calder~n (see [3]). R. COIFMAN - R. ROCHBERG - G. 2) is satisfied by Uj for all integers j (with c = 1). Thus, the last expression is dominated by We thus have obtained the extension of von Neumann's inequality for positive contractions. e. 3» can be extended to subpositive contractions. 3) can be changed to obtain the more general result.

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A new approach to linear filtering and prediction problems by Kallenrode

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