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Full-Text Articles in Other Mathematics
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 …
Invariant Basis Number And Basis Types For C*-Algebras, Philip M. Gipson
Invariant Basis Number And Basis Types For C*-Algebras, Philip M. Gipson
Department of Mathematics: Dissertations, Theses, and Student Research
We develop the property of Invariant Basis Number (IBN) in the context of C*-algebras and their Hilbert modules. A complete K-theoretic characterization of C*- algebras with IBN is given. A scheme for classifying C*-algebras which do not have IBN is given and we prove that all such classes are realized. We investigate the invariance of IBN, or lack thereof, under common C*-algebraic construction and perturbation techniques. Finally, applications of Invariant Basis Number to the study of C*-dynamical systems and the classification program are investigated.
Adviser: David Pitts