Abstract
This is a résumé of A. Pietsch’s concept of related linear operators in the study of spectral properties and homomorphism theorems forp-bounded linear operators on Mackey-complete topological vector spaces. It turns out that many results proved by various authors in the setting of Mackey-complete topological vector spaces follow directly from the corresponding classical results by means of purely algebraic relations.
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Literatur
G. R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. 15, 399–421 (1965)
M. Altman, On linear functional equations in locally convex linear spaces, Studia Math. 13, 194–207 (1953)
A. Deprit, Contribution a l’etude de l’algebre des applications lineaires continues d’un espace localement convex separe, Acad. Roy. de Belgique Coll. in 80 cl. des sciences Ser. 2, 31, 1–170 (1959/60)
N. Dunford, Spectral theory. I Convergence to projections, Trans. A.M.S. 54, 185–217 (1943)
B. Gramsch, Integration und holomorphe Funktionen in lokal - beschränkten Räumen, Math. Ann. 162, 190–210 (1965)
T. Kato, Perturbation theory for nullity, defiency and other quantites of linear operators, Journ. d’Analyse Math. 6, 261–322 (1958)
G. Köthe, Topologische lineare Räume I, Grundlehren der math. Wissenschaften 107: Springer 1966
H. Kroh, LT. Mertins, Ein Homomorphiesatz und verwandte Operatoren in topologischen Vektorräumen, Manuscripta Math. 25, 241–247 (1978)
D. C. Lay, Spectral analysis using ascent, descent, nullity and defect. Math. Ann. 184, 197–214 (1970)
U. Mertins, Verwandte Operatoren, Math. Z. 159, 107–121 (1978)
G. Neubauer, Zur Spektraltheorie in lokalkonvexen Algebren, Math. Ann. 142, 131–164 (1961)
A. Pietsch, Zur Fredholmschen Theorie in lokalkonvexen Räumen, Studia Math. 22, 161–169 (1963)
H. H. Schaefer, On the Fredholm alternative in locally convex linear spaces, Studia Math. 18, 229–245 (1955)
H. H. Schaefer, Topological vector spaces, Grad. Texts in Math. 3: Springer 1971
P. Uss, Sur les operateurs bornés dans les espaces localement convexes, Studia Math. 37, 139–158 (1971)
H.-D. Wacker, Über die Verallgemeinerung eines Satzes von Kato, Math. Z. 190, 55–61 (1985)
L. Waelbroeck, Le calcul symbolique dans les algebres commutatives, Journ. de Math. Pures et Appl. 33, 147–186 (1954)
V. Wrobel, Spektraltheorie beschränkter Operatoren in lokalkonvexen Räumen, Math. Nachr. 80, 151–156 (1977)
Ders., Spektraltheorie stetiger Endomorphismen eines lokalkonvexen Raumes, Math. Ann. 234, 193–208 (1978)
Ders., Strikt singuläre Operatoren in lokalkonvexen Räumen. II Beschränkte Operatoren, Math. Nachr. 110, 205–213 (1983)
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Von Wrobel, V. Spektraltheorie verwandter operationen. Abh.Math.Semin.Univ.Hambg. 57, 179–192 (1987). https://doi.org/10.1007/BF02941609
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DOI: https://doi.org/10.1007/BF02941609