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Keywords:
locally convex space; $\text{\rm H}$-locally convex space; numerical range; spectrum
locally convex space; $\text{\rm H}$-locally convex space; numerical range; spectrum
Summary:
The spatial numerical range for a class of operators on locally convex space was studied by Giles, Joseph, Koehler and Sims in [3]. The purpose of this paper is to consider some additional properties of the numerical range on locally convex and especially on $\text{\rm H}$-locally convex spaces.
References:
[1] Bonsal F.F., Duncan J.: Numerical range of operators on normed spaces and of elements of normed algebras. London Math. Soc. Lecture Note Series 2, Cambridge, 1971. MR 0288583
[2] Bonsal F.F., Duncan J.: Numerical ranges II. London Math. Soc. Lecture Note Series 10, Cambridge, 1973. MR 0442682
[3] Giles J.R., Joseph G., Koehler D.O., Sims B.: On numerical ranges of operators on locally convex spaces. J. Austral. Math. Soc. 20 (1975), 468-482. MR 0385598 | Zbl 0312.47002
[4] Hildebrandt S.: Über den numerischen Werterbereich eines Operators. Math. Annalen 163 (1966), 230-247. MR 0200725
[5] Joseph G.A.: Boundedness and completeness in locally convex spaces and algebras. J. Austral. Math. Soc. 24 (1977), 50-63. MR 0512300 | Zbl 0367.46045
[6] Kramar E.: Locally convex topological vector spaces with Hilbertian seminorms. Rev. Roum. Math. pures et Appl. 26 (1981), 55-62. MR 0616022 | Zbl 0457.46001
[7] Kramar E.: Linear operators in $H$-locally convex spaces. ibid. 26 (1981), 63-77. MR 0616023 | Zbl 0457.46002
[8] Precupanu T.: Sur les produits scalaires dans des espaces vectoriels topologiques. ibid. 13 (1968), 83-93. MR 0235398 | Zbl 0155.45201
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