Previous |  Up |  Next

Article

Keywords:
locally convex space; triangularization; invariant subspace; compact operator; quasinilpotent operator
Summary:
Some results concerning triangularization of some operators on locally convex spaces are established.
References:
[1] Edwards R.E.: Functional Analysis, Theory and Applications. Holt, Reinehart and Winston, New York, 1965. MR 0221256 | Zbl 0189.12103
[2] Floret K., Wloka J.: Einführung in die Theorie der lokalkonvexen Räumen. Springer-Verlag, Berlin, Heidelberg, New York, 1968. MR 0226355
[3] Grabiner S.: The nilpotency of Banach nil algebras. Proc. Amer. Math. Soc. 21 (1969), 510. MR 0236700 | Zbl 0174.44602
[4] Hadwin D., Nordgren E., Radjabalipour M., Radjavi H., Rosenthal P.: On simultaneous triangularization of collection of operators. Houston J. Math. 17 (1991), 581-602. MR 1147275
[5] Katavolos A., Radjavi H.: Simultaneous triangulation of operators on a Banach space. J. London Math. Soc. 41 (1990), 547-554. MR 1072047
[6] Kramar E.: Invariant subspaces for some operators on locally convex spaces. Comment. Math. Univ. Carolinae 38 (1997), 635-644. MR 1601676 | Zbl 0937.47005
[7] Litvinov G.L., Lomonosov V.I.: Density theorems in locally convex spaces and theirs applications (in Russian). Trudi sem. vekt. i tenz. analiza 20 (1981), 210-227. MR 0622018
[8] Lomonosov V.I.: Invariant subspace of operators commuting with compact operators. Funct. Anal. Appl. 7 (1973), 213-214. MR 0420305
[9] Ma T.W.: On rank one commutators and triangular representations. Canad. Math. Bull. 29 (1986), 268-273. MR 0846703 | Zbl 0555.47004
[10] Mendoza R.V.: The $(\Gamma , t)$-topology on $L(E,E)$ and the spectrum of a bounded linear operator on a locally convex topological vector space. Bol. Soc. Mat. Mexicana 3 (1997), 151-164. MR 1452669 | Zbl 0905.46004
[11] Radjavi H., Rosenthal P.: From local to global triangularization. J. Funct. Anal. 147 (1997), 443-456. MR 1454489 | Zbl 0902.47019
[12] Ringrose J.R.: Super-diagonal forms for compact linear operators. Proc. London Math. Soc. (3) 12 (1962), 367-384. MR 0136998 | Zbl 0102.10301
[13] Uss P.: Sur les opérateurs bornés dans les espaces localement convexes. Studia Math. 37 (1971), 139-158. MR 0303328 | Zbl 0212.15901
Partner of
EuDML logo