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Infinite-factorable holomorphic mappings on locally convex spaces. (English) Zbl 0646.46039

We introduce the notion of holomorphic mappings of uniformly bounded A- type between locally convex spaces where A denotes any normed operator ideal in the sense of A. Pietsch. In this note we consider such holomorphic mappings for the operator ideals \(L_{\infty}\), \(S_{\infty}\) and \(K_{\infty}\), respectively, of all \(\infty\)- factorable, strongly \(\infty\)-factorable and \(\infty\)-compact operators.

MSC:

46G20 Infinite-dimensional holomorphy
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
47L10 Algebras of operators on Banach spaces and other topological linear spaces
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