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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.
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
Full Text: DOI
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