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A useful algebra for functional calculus. (English) Zbl 07088838
Summary: We show that some unital complex commutative \(\mathrm{LF}\)-algebra of \(\mathcal{C}^{(\infty)}\) \(\mathbb{N}\)-tempered functions on \(\mathbb{R}^+\) [M. Hemdaoui, Sarajevo J. Math. 13(25), No. 1, 61–70 (2017; Zbl 1424.46072)] equipped with its natural convex vector bornology is useful for functional calculus.
MSC:
46A08 Barrelled spaces, bornological spaces
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46A17 Bornologies and related structures; Mackey convergence, etc.
47A60 Functional calculus for linear operators
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