Degree theory for (S+) mappings in non-reflexive banach spaces

Let E be a real Banach space, E∗ the dual space of E, E∗∗ the dual space of E∗ and Ω⊂E∗∗ an open bounded subset, and let T:Ω¯→2E∗ be a weak compact mapping of class (S+) (see Definition 1.2). We will construct a degree theory for such a mapping.