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

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 concept and partial differential equations; of the fashionable worldwide method of topology and geometry; of illustration idea and harmonic research; and of dynamical structures and mathematical physics. the current selection of papers represents contributions to a convention, they usually were rigorously chosen which will bridging varied yet similar components of arithmetic that have only in the near past displayed an unforeseen community of interconnections, in addition to new and fascinating cross-fertilizations. Our unify­ ing subject is the algebraic view and method of the research of operators and their functions. The complementarity among the range of issues at the one hand and the solidarity of rules at the different has been under pressure. many of the longer contributions characterize fabric from lectures (in extended shape and with proofs for the main part). besides the fact that, the shorter papers, in addition to the longer ones, are a vital part of the image; they've got all been conscientiously refereed and revised to be able to a cohesion of objective, timeliness, clarity, and large attraction. Raul Curto and Paile E. T.

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In [1], Apostol and Fialkow showed that for A = B(H), H a Hilbert space, if {BI,B 2 , ••• ,Bn} is linearly independent modulo K(H), the ideal of compact operators, then Ran(R(A, c I if and only if Ai E I, i = 1,2, ... , n. In this note, we examine a somewhat different problem. If C is a subalgebra of A, define Ec(A) to be the algebra of elementary operators on A which leave C invariant. =l MA;,B; such that MA;,B; E Ec(A), i = 1,2, ... ,n? ~A,B = = = = B» = KJ. Coates 50 We give an example where the answer to the above question is negative.

Is non-zero and finite. We define a nest 13 to be of order type I I if it is not of order type I. Since there is not non-zero finite projection in type I I I factor and, there is no infinite projection in type I II factor, so all nests in type I II or type I I I factors are of order type I I. In [7] we have proven that the property that a nest 13 is of order type I I is a necessary and sufficient condition for a (type I I or type I I I) factor M to be a norm-principal bimodule of algf3. As a corollary, we proved that any separably acting type I II or type I I I factor is always a norm-closed singly generated bimodule of an arbitrary nest sub algebra in the factor.

Soc. 290 (1985),415-429. [5] __, The range inclusion problem for elementary operators, Michigan Math. J. 34 (1987),451-459. [6] L. A. Fialkow and R. Loebl. Elementary mappings into ideals of operators, Illinois J. Math. 28, 555-578. K. Fong and A. R. Sourour, On the operator identity L: AkX Bk == 0, Can. J. Math. 31 (1979),845-857. Questions on Bimodules of Nest Algebras Xingde DaP the University of North Carolina at Charlotte, Charlotte, NC 28223 Abstract We will describe some recent results on bimodules of nest algebras and we will propose some related questions.

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