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.
@article{118576, author = {Edvard Kramar}, title = {On the numerical range of operators on locally and on H-locally convex spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {229-237}, zbl = {0806.47003}, mrnumber = {1241732}, language = {en}, url = {http://dml.mathdoc.fr/item/118576} }
Kramar, Edvard. On the numerical range of operators on locally and on H-locally convex spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 229-237. http://gdmltest.u-ga.fr/item/118576/
Numerical range of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lecture Note Series 2, Cambridge, 1971. | MR 0288583
Numerical ranges II, London Math. Soc. Lecture Note Series 10, Cambridge, 1973. | MR 0442682
On numerical ranges of operators on locally convex spaces, J. Austral. Math. Soc. 20 (1975), 468-482. (1975) | MR 0385598 | Zbl 0312.47002
Über den numerischen Werterbereich eines Operators, Math. Annalen 163 (1966), 230-247. (1966) | MR 0200725
Boundedness and completeness in locally convex spaces and algebras, J. Austral. Math. Soc. 24 (1977), 50-63. (1977) | MR 0512300 | Zbl 0367.46045
Locally convex topological vector spaces with Hilbertian seminorms, Rev. Roum. Math. pures et Appl. 26 (1981), 55-62. (1981) | MR 0616022 | Zbl 0457.46001
Linear operators in $H$-locally convex spaces, ibid. 26 (1981), 63-77. (1981) | MR 0616023 | Zbl 0457.46002
Sur les produits scalaires dans des espaces vectoriels topologiques, ibid. 13 (1968), 83-93. (1968) | MR 0235398 | Zbl 0155.45201