We have studied diagonal operators on Hilbert space and some classes of Banach spaces.On the Hilbert space l2 we give the necessary and sufficient conditions for the diagonal operators to have hyperful orbits, that is,orbits where every subsequence spans the whole space. A consequence of this characterization is that for diagonal operators, either all cyclic vectors have hyperful orbits or none of the cyclic vectors has a hyperful orbit. Then, we extend some of these results to the spaces c0, C(0; 1), and L2[0; 1].On L2[0; 1] we consider a Multiplication Operator in place of a Diagonal Operator. We also study the case with complex scalars, we show that on every separable Banach space there are operators with hyperful orbits.
|Commitee:||Enflo, Per, Janson, Thomas, Lomonosov, Victor, Portman, John, Zvavitch, Artem|
|School:||Kent State University|
|Department:||College of Arts and Sciences / Department of Mathematical Science|
|School Location:||United States -- Ohio|
|Source:||DAI-B 78/11(E), Dissertation Abstracts International|
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