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Extra resources for (A, B)-Invariant Polyhedral Sets of Linear Discrete-Time Systems
Two pairs (F , a) and (F 7, a ') are said to be isomorphic if there is an isomorphism h: E —> F 7 1. C *-ALGEBRAS AND K -THEORY 20 in the category C such that the diagram E —^ E ' a a' h E E' commutes. The direct sum defines the operation of addition of pairs. A pair (E, a) is said to be elementary if the automorphism a is homotopic to Id# in the set of automorphisms of E. £, a )} with respect to the following equivalence relation: cr ~ cr7 if and only if there are elementary pairs r and r ' such that a + r is isomorphic to cr' + r'.
B ^ y (X) is a Banach category. P roof. The module K (M, N) is just equal to C(X,ICB(P,Q)) (Banach Csubmodule of MorB~>(X)(M, N)). Hence, the quotient module of the space of mor phisms by /C is a Banach space. Since ICB(HB) is a two-sided ideal, the construction is compatible with compositions. 83. The category B ^ y (X) is isomorphic to the category HB(X) of locally trivial bundles over X constructed from the Banach category HyB . 3. 84 (). Let V be an arbitrary category, and let E and F be objects of V.
As usual, we can identify r G(Hom(£7,F)) with the set of all G-A-morphisms ip: £7 —» F. 15, we obtain the following assertion. 16. Let ip': E\y —> F\y be a morphism of the restrictions of the G-A-bundles E and F over a compact space X to a closed G-stable subset Y. Then tp' can be extended to a morphism of G-A-bundles ip: £7 —> F over X . If