Spectra of Abelian C*-Subalgebra Sums

Let $C_b(X)$ be the C*-algebra of bounded continuous functions on some non-compact, but locally compact Hausdorff space $X$. Moreover, let $A_0$ be some ideal and $A_1$ be some unital C*-subalgebra of $C_b(X)$. For $A_0$ and $A_1$ having trivial intersection, we show that the spectrum of their vector space sum equals the disjoint union of their individual spectra, whereas their topologies are nontrivially interwoven. Indeed, they form a so-called twisted-sum topology which we will investigate before. Within the whole framework, e.g., the one-point compactification of $X$ and the spectrum of the algebra of asymptotically almost periodic functions can be described.Comment: 12 pages, LaTeX. Extension of Section 3 in arXiv:1010.0449 (version v1

Stratification of the Generalized Gauge Orbit Space

The action of Ashtekar's generalized gauge group \Gb on the space \Ab of generalized connections is investigated for compact structure groups \LG. First a stratum is defined to be the set of all connections of one and the same gauge orbit type, i.e. the conjugacy class of the centralizer of the holonomy group. Then a slice theorem is proven on \Ab. This yields the openness of the strata. Afterwards, a denseness theorem is proven for the strata. Hence, \Ab is topologically regularly stratified by \Gb. These results coincide with those of Kondracki and Rogulski for Sobolev connections. As a by-product, we prove that the set of all gauge orbit types equals the set of all (conjugacy classes of) Howe subgroups of \LG. Finally, we show that the set of all gauge orbits with maximal type has the full induced Haar measure 1.Comment: LaTeX, 21 page