Simultaneousely Triangularization of Families of Compact Operators on the Banach Spaces

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Behmani, Reza | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41282 (02)
University: Sharif University of Technology
Department: Mathematical Science
Advisor(s): Fanai, Hamid Reza
Abstract:
Simultaneous triangulation of matrices is a subject with a rich literature. There are many well known theorems available, such as McCoy theorem or Burnsides. In the nite dimensional case since the all the topologies on vector spaces are the same, there is a little bit diculty and most of the arguments are from linear algebra. In this thesis we study the simultaneous triangulation of sub algebras of K(X),with X a innite dimensional Banach space. We will give a denition of simultaneous triangulation which is independent of the notion of Basis and totally relies on Invariant subspaces. This denition coincides with the denition of simultaneous triangulation in nite dimensional case. Then we will generalize many theorems of simultaneous triangulation for subalgebras of B(Cn) to the sub algebras of K(X) (Under certain conditions). McCoy theorem and Block simultaneous triangulation theorem are examples of such generalizations
Keywords:
Banach Spaces ; Compact Operators ; Invariant Subspace ; Triangularizing Chain ; Simultaneous Triangularization

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