The gap between unbounded regular operators

Abstract

We study and compare the gap and the Riesz topologies of the space of all unbounded regular operators on Hilbert C*-modules. We show that the space of all bounded adjointable operators on Hilbert C*-modules is an open dense subset of the space of all unbounded regular operators with respect to the gap topology. The restriction of the gap topology on the space of all bounded adjointable operators is equivalent with the topology which is generated by the usual operator norm. The space of regular selfadjoint Fredholm operators on Hilbert C*-modules over the C*-algebra of compact operators is path-connected with respect to the gap topology, however, the result may not be true for some Hilbert C*-modules.

14 pages, accepted

References in corpus (6)

• Frames in Hilbert C*-modules and C*-algebras
• On the space of Fredholm operators
• Adjointability of densely defined closed operators and the Magajna-Schweizer Theorem
• Generalized inverses and polar decomposition of unbounded regular operators on Hilbert $C^{\ast }$-modules
• Regular Operators on Hilbert C^*-modules
• The Atkinson Theorem in Hilbert C*-Modules Over C*-Algebras of Compact Operators

Cited by in corpus (4)

• Moore-Penrose inverse of Gram operator on Hilbert C*-modules
• Normality of adjointable module maps
• The index formula and the spectral shift function for relatively trace class perturbations
• Stability of Fredholm property for regular operators on Hilbert $C^{\ast }$-modules