| description: |
This project is a successor of Target Funding Project No 0085. The investigations on the homological classification of monoids and polynomial completeness of algebras are continued with an emphasis on the category theoretic aspect of the results. Interaction between different versions of approximation property of the Banach spaces and the geometric properties of the spaces of operators which act in those spaces is investigated. Relationships between approximation property and the approximation of weakly compact operators in strong operator topology are systematically studied. New methods of the theory of sequence spaces are developed (generalizations of the Hahn property, dual pairs of sequence spaces and summability envelopes). The possibility of extending the classical results of the Banach algebras theory to more general topological algebras is studied. New efficient solution methods of equations appearing in acoustics and electromagnetism theory are developed and the properties of solutions are investigated. Semisymmetric Riemann manifolds are classified with special attention to their semiparallel embedding into space forms. In connection with invariant differential calculus the universal structure of jet bundles of smooth mappings is studied. A higher order exterior calculus is constructed with the results being applied to theoretical physics and to the theory of hypersymmetries, in particular. |