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

ISBN-10: 1461202558

ISBN-13: 9781461202554

ISBN-10: 1461266831

ISBN-13: 9781461266839

The idea of operators stands on the intersection of the frontiers of recent research and its classical opposite numbers; of algebra and quantum mechanics; of spectral concept and partial differential equations; of the fashionable international method of topology and geometry; of illustration concept and harmonic research; and of dynamical structures and mathematical physics. the current number of papers represents contributions to a convention, and so they were conscientiously chosen in an effort to bridging assorted yet similar components of arithmetic that have just recently displayed an unforeseen community of interconnections, in addition to new and fascinating cross-fertilizations. Our unify ing topic is the algebraic view and method of the learn of operators and their purposes. The complementarity among the variety of subject matters at the one hand and the harmony of principles at the different has been under pressure. many of the longer contributions symbolize fabric from lectures (in increased shape and with proofs for the main part). although, 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 charm. Raul Curto and Paile E. T.

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So it is not a norm-principal bimodule of algC. Is the converse true? In particular, Question 5 If the CSL is a tensor product of two nests. b. of algC. Using Larson-Pitts' factorization results ([13] [16]) and David Larson's technique (cf. 9) one can prove a generalization of the 'weak' factorization of a nest algebra. Namely, for an arbitrary nest {3 in a separably acting factor M, for each positive invertible operator P E M, there exist operators A and B in alg{3, which are invertible in M but not necessarily invertible in alg{3, such that P factors in the form of AA* and B* B.

They proved that each strong closed bimodule is singly generated under the strong topology. In a conversation, Arveson suggested to the author the following question. Question 3 Classify the norm-closed bimodules of nest algebras. Questions on bimodules of nest algebras 55 This question is open even in B(1i) case. Recently Orr classified the maximal ideals and the automorphism invariant ideals of continuous nest algebras. Question 4 Extend above results on bimodules and Jacobson radicals into CSL-algebras.

Hypercontractions and subnormality, J. Operator Theory 13(1985), 203-217. , On the intertwining of joint isometries, J. Operator Theory 23(1990), 339--350. , Model theory on the unit ball in Theory (to appear). [CuVa] Curto, R. E. , Automorphism invariance of the operator-valued Poisson transform, Acta Scient. Math. (to appear). on, J. -H. , A generalization of von Neumann's inequality to complex ball, Proc. Amer. Math. Soc. 68(1978),300-304. [MiiVa] Standard models for some commuting multioperators, Proc.

### Algebraic Methods in Operator Theory by Radu Gadidov (auth.), Raúl E. Curto, Palle E. T. Jørgensen (eds.)

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