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Decomposable Functions And Universal C*-Algebras, Llolsten Kaonga

Doctoral Dissertations

This paper deals with universal $C\sp\*$-algebras generated by matricial relations on the generators, for example, the universal $C\sp\*$-algebra with generators $a\sb{ij}, 1 \leq i,j \leq n$, subject to the condition that the matrix ($a\sb{ij}$) be normal and have spectrum in a designated compact subset ${\cal K}$ of the complex plane.

The main thrust of the paper is to compute the K-groups of some of these $C\sp\*$-algebras and to determine when they contain non-trivial projections. In the above example, we show that the K-groups of the algebra coincide with the topological K-groups of the set ${\cal K}$. We show, in general, …

Stability Properties For The Constant Of Hyperreflexivity, Ileana Ionascu

Doctoral Dissertations

Let H be a separable, complex, Hilbert space and let ${\cal B}(H$) be the algebra of all (bounded linear) operators on H. We define a function$$\kappa:{\cal B}(H) \to \lbrack 1,\infty\rbrack;\qquad \kappa(T) = K({\cal A}\sb{w}(T)),\qquad \forall T \in {\cal B}(H),$$where ${\cal A}\sb{w}(T$) is the unital weakly closed algebra generated, in ${\cal B}(H$), by T, and $K({\cal A}\sb{w}(T$)) is the constant of hyperreflexivity of ${\cal A}\sb{w}(T$). If H is finite-dimensional, we show that $\kappa$ is continuous at $T \in {\cal B}(H$) if and only if T is non-reflexive or has dimH distinct eigenvalues (Theorem 2.6). An auxiliary result (Theorem 2.1) states that …

On The Berezin Symbol, Semra Kilic-Bahi

Doctoral Dissertations

Let ${\cal H}$ be a functional Hilbert space of analytic functions on a complex domain $\Omega,$ with the normalized reproducing kernel function $k\sb{z},\ z\in\Omega.$ If A is a linear map of ${\cal H}$ into itself, the Berezin symbol, A, of A is defined on $\Omega$ by $\tilde{A}(z) = \langle Ak\sb{z},\ k\sb{z}\rangle.$ The purpose of this research is to study how the properties of an operator are reflected in the properties of its Berezin symbol. In summary, I have (1) studied the properties of the Berezin symbol as a complex-valued function; (2) characterized multiplication operators, induced by a multiplier of ${\cal …

Reflexive Subspaces And Lattices Of Pairs Of Projections, Deborah Narang

Doctoral Dissertations

Consider the sets ${\cal P}\sb{\cal H}$ and ${\cal P}\sb{\cal K}$ of the projections onto closed subspaces of Hilbert spaces ${\cal H}$ and $\cal K$ respectively. From the usual partial orders (based upon set containment) on $\cal P\sb{\cal K}$ and $\cal P\sb{\cal H}$, we can define a partial order on $\cal P\sb{\cal K}\times\cal P\sb{\cal H}$ by ($Q\sb1,P\sb1)\le(Q\sb2, P\sb2)$ if and only if $P\sb1\le P\sb2$ and $Q\sb2\le Q\sb1.$ Then the map $\alpha : \cal P\sb{\cal K}\times \cal P\sb{\cal H}\to \cal P\sb{\cal K\oplus\cal H}$ given by $\alpha(Q,P)=(1-Q)\oplus P$ is an order-preserving map. In particular, if $\cal L\subseteq\cal P\sb{\cal K\times\cal H}$ is a lattice, …