A generalized topological degree in admissible linear spaces (Q1898771)

Summary: The paper deals with the construction of a degree which extends the generalized topological degree of Browder and Petryshyn to admissible linear spaces introducing the notion of approximation nets and approximation-compact maps. After discussing the usual properties of a degree the relationship between approximation compactness and the concept of condensing maps is analysed. The non-locally convex spaces \(\ell^p\), \(H^p\), \(N^+\), \(L_p [0,1]\) and \(S[0,1]\) \((0 < p < 1)\) are considered for illustration. The main results are fixed-point theorems for these spaces. Concrete examples of operators are given for \(\ell^p\) and \(H^p\).