Projective Space of a C*-module

E. ANDRUCHOW, G. CORACH Y D. STOJANOFF

INFINITE DIMENSIONAL ANALYSIS, QUANTUM PROBABILITY AND RELATED TOPICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2001 vol. 4 p. 289 - 307

0219-0257

Let $X$ be a right Hilbert C$^*$-module over $A$. We study the geometry and the topology of the projective space ${cal P}(X)$ of $X$, consisting of the orthocomplemented submodules of $X$ which are generated  by a single element. We also study the geometry of the $p$-sphere$S_p(X)$ and the natural fibration $S_p(X) o {cal P}(X)$, where  $S_p(X)={xin X :  langle x,x angle =p}$, for $pin A$ a projection. The projective space and the $p$-sphere are shown to be homogeneous differentiable spaces of the unitary group of the algebra ${{cal L}}_A(X)$ of adjointable operators of $X$. The homotopy theory of these spaces is examined.