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## Studia Mathematica

2000 | 140 | 2 | 163-175
Tytuł artykułu

### Restriction of an operator to the range of its powers

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EN
Abstrakty
EN
Let T be a bounded linear operator acting on a Banach space X. For each integer n, define $T_n$ to be the restriction of T to $R(T^n)$ viewed as a map from $R(T^n)$ into $R(T^n)$. In [1] and [2] we have characterized operators T such that for a given integer n, the operator $T_n$ is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where $T_n$ belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with topological uniform descent.
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Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
163-175
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-28
poprawiono
1999-10-01
Twórcy
autor
Bibliografia
• [1] M. Berkani, On a class of quasi-Fredholm operators, Integral Equations Oper. Theory 34 (1999), 244-249.
• [2] M. Berkani and M. Sarih, On semi-B-Fredholm operators, submitted.
• [3] S. R. Caradus, Operator Theory of the Pseudo-Inverse, Queen's Papers in Pure and Appl. Math. 38 (1974), Queen's Univ., 1974.
• [4] S. Grabiner, Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317-337.
• [5] R. Harte, On Kato non-singularity, Studia Math. 117 (1996), 107-114.
• [6] R. Harte and W. Y. Lee, A note on the punctured neighbourhood theorem, Glasgow Math. J. 39 (1997), 269-273.
• [7] M. A. Kaashoek, Ascent, descent, nullity and defect, a note on a paper by A. E. Taylor, Math. Ann. 172 (1967), 105-115.
• [8] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261-322.
• [9] J. J. Koliha, M. Mbekhta, V. Müller and P. W. Poon, Corrigendum and addendum: "On the axiomatic theory of spectrum II", Studia Math. 130 (1998), 193-198.
• [10] V. Kordula and V. Müller, On the axiomatic theory of spectrum, ibid. 119 (1996), 109-128.
• [11] J. P. Labrousse, Les opérateurs quasi-Fredholm: une généralisation des opérateurs semi-Fredholm, Rend. Circ. Mat. Palermo (2) 29 (1980), 161-258.
• [12] M. Mbekhta and M. Müller, On the axiomatic theory of spectrum II, Studia Math. 119 (1996), 129-147.
• [13] P. W. Poon, Spectral properties and structure theorems for bounded linear operators, thesis, Dept. of Math. and Statist., Univ. of Melbourne, 1997.
• [14] C. Schmoeger, On a class of generalized Fredholm operators, I, Demonstratio Math. 30 (1997), 829-842.
• [15] C. Schmoeger, On a class of generalized Fredholm operators, V, ibid. 32 (1999), 595-604.
• [16] C. Schmoeger, On a generalized punctured neighborhood theorem in ℒ(X), Proc. Amer. Math. Soc. 123 (1995), 1237-1240.
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Bibliografia
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