7. An invertibility symbol calculus for the C*-algebra Uarc8. The C*-algebra Barc; 9. The C*-algebra B; 10. Invertibility of functional operators; 11. The C*-algebra B; Acknowledgment; References; Non-Hermitian Quantum Mechanics of Bosonic Operators; 1. Introduction; 2. Preliminaries; 3. Non self-adjoint Hamiltonian H describing two interacting bosonic operators; 3.1. Model; 3.2. Spectrum; 4. Accretivity; 4.1. Eigenvectors and eigenvalues of H; 4.2. Eigenfunctions and eigenvalues of H*; 4.3. Biorthogonality of the eigenfunctions; 4.4. Completeness of the eigenfunctions

4.5. Asymptotic behavior of the eigenfunctions4.6. Metric operator; 4.7. Physical Hilbert space; 5. Conclusions; References; Fredholm Conditions on Non-compact Manifolds: Theory and Examples; 1. Introduction; 1.1. Background and main result; 1.2. Exhaustive families of representations; 1.3. Fredholm Lie groupoids; 1.4. Examples and applications; 1.5. Contents of the paper; 2. Groupoids and their C*-algebras; 2.1. Locally compact groupoids; 2.2. Haar systems and C*-algebra; 2.3. Manifolds with corners and Lie groupoids; 2.4. Examples of Lie groupoids

3. Exhaustive families of representations and Exel's question3.1. Exhaustive families of representations of C*-algebra; 3.2. Exel's question and properties; 4. Fredholm conditions; 4.1. Fredholm groupoids and their characterization; 4.2. Pseudodifferential operators; 5. Examples; 5.1. Examples related to group actions; 5.2. The edge groupoid; 5.3. Desingularization groupoids; 5.4. Desingularization and singular spaces; Acknowledgment.; References; Statistical e-Convergence of Bögel-Type Continuous Functions; 1. Introduction and Preliminaries; 2. A Korovkin-type approximation theorem