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Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert
Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert
Department of Mathematics: Dissertations, Theses, and Student Research
This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δD which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.
A first application of kernel stabilization for δD shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a sufficient condition …
Operator Algebras Generated By Left Invertibles, Derek Desantis
Operator Algebras Generated By Left Invertibles, Derek Desantis
Department of Mathematics: Dissertations, Theses, and Student Research
Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*-algebras. Representations of such algebras encode the dynamics of orthonormal sets in a Hilbert space.We instigate a research program on concrete operator algebras that model the dynamics of Hilbert space frames.
The primary object of this thesis is the norm-closed operator algebra generated by a left invertible $T$ together with its Moore-Penrose inverse $T^\dagger$. We denote this algebra by $\mathfrac{A}_T$. In the isometric case, $T^\dagger = T^*$ and $\mathfrac{A}_T$ is a representation of the Toeplitz algebra. Of particular interest …