Differential geometry of spaces of relatively regular operators
Let A be a Banach algebra with group of units G and with the set of idempotents Q. The authors study the topological and geometric properties of the space \(S=\{(a,b)\in A\times A:\) \(ar=a\), \(rb=b\), \(ba=r\}\), where r is a fixed element in Q. In particular they study principal fiber bundles \(\tau: G\to S\), where \(\tau (g)=(ga_ 0,b_ 0g^{-1}),\) \((a_ 0,b_ 0)\in S\), and \(\theta: S\to Q,\) where \(\theta ((a,b))=ab.\) When A is a \(C^*\)-algebra and \(r=r^*\), they study also a real analytic retraction of S onto \(\{\) (a,b)\(\in S:\) \(b=a^*\}\). The authors announce further papers on similar topics.
scientific article; zbMATH DE number 4198818
scientific article