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Download Advances in Invariant Subspaces and Other Results of by Ernst Albrecht, Jörg Eschmeier (auth.), R. G. Douglas, C. M. PDF

By Ernst Albrecht, Jörg Eschmeier (auth.), R. G. Douglas, C. M. Pearcy, B. Sz.-Nagy, F.-H. Vasilescu, Dan Voiculescu, Gr. Arsene (eds.)

The annual Operator conception meetings, geared up via the dept of arithmetic of INC leisure and the collage of Timi?oara, are meant to advertise cooperation and alternate of knowledge among experts in all parts of operator idea. This quantity includes papers contributed through the contributors of the 1984 convention. They mirror a very good number of subject matters, handled by way of the trendy operator concept, together with very fresh advances within the invariant subspace challenge, subalgebras of operator algebras, hyponormal, Hankel and different distinctive sessions of operators, spectral decompositions, points of dilation concept etc. The learn contracts of the dept of arithmetic of INCREST with the nationwide Council for technological know-how and expertise of Romania supplied the ability for constructing the learn task in arithmetic; they characterize the beneficiant framework of those conferences, too. it truly is our excitement to recognize the monetary aid of UNESCO which additionally contibuted to the luck of this assembly. we're indebted to Professor Israel Gohberg for together with those complaints within the OT sequence and for helpful recommendation within the enhancing strategy. Birkhauser Verlag used to be very cooperative in publishing this quantity. Mariana Bota, Camelia Minculescu and Rodica Stoenescu handled the tricky job of typing the entire manuscript utilizing a Rank Xerox 860 observe processor; we thank them for the wonderful task they did.

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Read or Download Advances in Invariant Subspaces and Other Results of Operator Theory: 9th International Conference on Operator Theory, Timişoara, and Herculane (Romania), June 4–14, 1984 PDF

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Extra info for Advances in Invariant Subspaces and Other Results of Operator Theory: 9th International Conference on Operator Theory, Timişoara, and Herculane (Romania), June 4–14, 1984

Example text

F q ) for any q such that 0 < q < p ,we can m m m proceed as in the first part of the proof in order to get a unicellular operator T of the form T* m * o -q. t P). Clearly we have Lat T '" Lat T~ + w* n '" w m + Lat Y~ + w* n • • 54 REFERENCES 1. Barrla, J. : The invariant subspaces of a Volterra operator, J. Operator Theory, 6 (981), 341-349. 2. Barria, J. R. : Unicellular operators, Trans. Amer. Math. Soc. , 284(1984), 229-246. 17 © 1986 Birkhauser Verlag Basel ISOMETRIC DILATIONS OF COMMUTING CONTRACTIONS.

13]). It therefore follows from general principles that T is the adjoint of a bounded, linear, one-to-one mapping il>T : Q T - L 1/H~. 1. If T E (ACC), o(T)::::>T, and T is not an isometry, then T has a nontrivial hyperinvariant subspace. In view of this theorem we make the following definition. 2. We denote by A the class of all T in (ACC) such that T is an isometry. If TEA, then one knows that the range of T is all of AT and that T is a weak*-homeomorphism of H 00 onto AT (d. [13]).

3, let us introduce the linear subspace Z of Y given by m-l Z := {k~O skea k : m £ Nand a o '··· ,a m_ l £ ET(F)}. Again, it is not hard to see that (S - A)Z = Z holds for all A £ C \ F, which implies 6X T (F)C6E T(F)CZCE S(F) = YS(F). 3 of [5]. 7. In this connection, let us also refer to the various examples of super-decomposable operators in [13] to which this theorem applies. 3 of [7]. 8 need not be empty at all. 9. THEOREM. Assume that T £ L(X) is decomposable and S £ L(Y) is well- -decomposable.

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