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oai:docta.ucm.es:20.500.14352/575192023-08-10T20:51:49Zcom_20.500.14352_14col_20.500.14352_15

Composition operators between algebras of differentiable functions Llavona, José G. Gutiérrez, Joaquín M. 517.98 Differentiable mappings between banach spaces Algebras of differentiable functions Homomorphisms Composition operators Análisis funcional y teoría de operadores Let E, F be real Banach spaces, U subset-or-equal-to E and V subset-equal-to F non-void open subsets and C(k)(U) the algebra of real-valued k-times continuously Frechet differentiable functions on U, endowed with the compact open topology of order k. It is proved that, for m greater-than-or-equal-to p, the nonzero continuous algebra homomorphisms A: C(m)(U) --> C(p)(V) are exactly those induced by the mappings g: V --> U satisfying phi . g is-an-element-of C(p)(V) for each phi is-an-element-of E*, in the sense that A(f) = fog for every f is-an-element-of C(m)(U). Other homomorphisms are described too. It is proved that a mapping g: V --> E** belongs to C(k)(V, (E**, w*)) if and only if phi . g is-an-element-of C(k)(V) for each phi is-an-element-of E*. It is also shown that if a mapping g: V --> E verifies phi . g is-an-element-of C(k)(V) for each phi is-an-element-of E*, then g is-an-element-of C(k-1)(V, E). DGICYT Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:57:40Z 2023-06-20T16:57:40Z 1993-08 journal article https://hdl.handle.net/20.500.14352/57519 0002-9947 10.2307/2154428 eng PB 87-1031 restricted access application/pdf American Mathematical Society