By Radu Gadidov (auth.), Raúl E. Curto, Palle E. T. Jørgensen (eds.)

The concept of operators stands on the intersection of the frontiers of contemporary research and its classical opposite numbers; of algebra and quantum mechanics; of spectral idea and partial differential equations; of the trendy international method of topology and geometry; of illustration concept and harmonic research; and of dynamical platforms and mathematical physics. the current number of papers represents contributions to a convention, and so they were rigorously chosen so that it will bridging varied yet similar parts of arithmetic that have just recently displayed an unforeseen community of interconnections, in addition to new and interesting cross-fertilizations. Our unify ing subject matter is the algebraic view and method of the research of operators and their purposes. The complementarity among the range of subject matters at the one hand and the solidarity of principles at the different has been under pressure. a number of the longer contributions characterize fabric from lectures (in increased shape and with proofs for the main part). despite the fact that, the shorter papers, in addition to the longer ones, are an essential component of the image; they've got all been conscientiously refereed and revised so that it will a solidarity of objective, timeliness, clarity, and huge allure. Raul Curto and Paile E. T.

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4T3 z - ... for 11'1 < 1/ niax{r,IITII}. Since g is analytic on the disc V(O,l/r), it follows exactly as in the scalar-valued setting from Cauchy's integral formula that the preceding identity holds even for all I' E V(O,l/r). ) is 2: l/r. By the standard formula for the radius of convergence of a vector-valued power series, we conclude that PT(Z) $ r, which completes the proof. c(X, Y). Further, for closed F ~ C and any 0 $ r < 00, let Fr := {z E C : dist(z, F) $ r} = F+ V(O,r). 2 Proposition.

G. Miller and M. M. Neumann 36 New York, 1968. 9. J. Eschmeier, Operator decomposability and weakly continuous representations o/locally compact abelian groups, J. Operator Theory 7 (1982), 201-208. 10. _ _ _ , Spectral decompositions and decomposable multipliers, Manuscripta math. 51 (1985), 201-224. 11. _ _ _ , A nalytische Dualitat und Tensorprodukte in der mehrdimensionalen Spektraltheorie, Habilitationsschrift, vol. 42, Schriftenreihe des Math. Inst. Universitat Miinster, Miinster, 1987. 12.

NEUMANN ABSTRACT. This note centers around the class D(G) of decomposable measures on a locally compact abelian group G. This class is a large subalgebra of the measure algebra M(G), has excellent spectral properties, and is related to a number of concepts from commutative harmonic analysis. The discussion of D(G) in Section 1 is to illustrate this point. 1, which improves recent results from [19] and includes some new properties related to the involution of M(G). We shall present a different approach, which avoids previous tools like the hull-kernel topology [19], [23] or the spectral theory of several commuting operators [2], [10].