On the numerical range of operators on locally and on H-locally convex spaces

Edvard Kramar

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 229-237
  • ISSN: 0010-2628

Abstract

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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 -locally convex spaces.

How to cite

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Kramar, Edvard. "On the numerical range of operators on locally and on H-locally convex spaces." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 229-237. <http://eudml.org/doc/247487>.

@article{Kramar1993,
abstract = {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.},
author = {Kramar, Edvard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally convex space; $\text\{\rm H\}$-locally convex space; numerical range; spectrum; spatial numerical range; H-locally convex spaces},
language = {eng},
number = {2},
pages = {229-237},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the numerical range of operators on locally and on H-locally convex spaces},
url = {http://eudml.org/doc/247487},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Kramar, Edvard
TI - On the numerical range of operators on locally and on H-locally convex spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 229
EP - 237
AB - 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.
LA - eng
KW - locally convex space; $\text{\rm H}$-locally convex space; numerical range; spectrum; spatial numerical range; H-locally convex spaces
UR - http://eudml.org/doc/247487
ER -

References

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  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. MR0288583
  2. Bonsal F.F., Duncan J., Numerical ranges II, London Math. Soc. Lecture Note Series 10, Cambridge, 1973. MR0442682
  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. (1975) Zbl0312.47002MR0385598
  4. Hildebrandt S., Über den numerischen Werterbereich eines Operators, Math. Annalen 163 (1966), 230-247. (1966) MR0200725
  5. Joseph G.A., Boundedness and completeness in locally convex spaces and algebras, J. Austral. Math. Soc. 24 (1977), 50-63. (1977) Zbl0367.46045MR0512300
  6. Kramar E., Locally convex topological vector spaces with Hilbertian seminorms, Rev. Roum. Math. pures et Appl. 26 (1981), 55-62. (1981) Zbl0457.46001MR0616022
  7. Kramar E., Linear operators in -locally convex spaces, ibid. 26 (1981), 63-77. (1981) Zbl0457.46002MR0616023
  8. Precupanu T., Sur les produits scalaires dans des espaces vectoriels topologiques, ibid. 13 (1968), 83-93. (1968) Zbl0155.45201MR0235398

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