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Uniform ascent and descent of bounded operators
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1982 Volume 34 Issue 2 Pages 317-337
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- Published: 1982 Received: February 04, 1980 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H Bart and D.C. Lay, Poles of a generalized resolvent operator, Proc. Roy. Irish Acad. Sect. A, 1974, 147-168.
2) S.R. Caradus, W.E. Pfaffenberger and B. Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, 9, Marcel Dekker, New York, 1974.
3) P.A. Fillmore and J.P. Williams, On operator ranges, Advances in Math., 7 (1971), 254-281.
4) K.H. Förster, Über die Invarianz einiger Räume, die zum Operator T-λA gehören, Arch. Math., 17 (1966), 56-64.
5) T.W. Gamelin, Decomposition theorems for Fredholm operators, Pacific J. Math., 15 (1965), 97-106.
6) S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966.
7) M.A. Gol'dman and S.N. Krackovskii, Invariance of certain spaces connected with the operator A-λI, Soviet Math. Dokl., 5 (1964), 102-104.
8) MA. Gol'dman and S.N. Krackovskii, Some perturbations of a closed linear operator, Soviet Math. Dokl., 5 (1964), 1243-1245.
9) S. Grabiner, Ranges of products of operators, Canad. J. Math., 26 (1974), 1430-1441.
10) S. Grabiner, Finitely generated, Noetherian, and Artinian Banach modules, Indiana Univ. Math. J., 26 (1977), 413-425.
11) S. Grabiner, Ascent, descent, and compact perturbations, Proc. Amer. Math. Soc., 71 (1978), 79-80.
12) S. Grabiner, Spectral consequences of the existence of intertwining operators, Comment. Math. Prace Mat., to appear.
13) B.E. Johnson and A.M. Sinclair, Continuity of linear operators commuting with continuous linear operators II, Trans. Amer. Math. Soc., 146 (1969), 533-540.
14) M.A. Kaashoek, Stability theorems for closed linear operators, Nederl. Akad. Wetensch. Proc. Ser. A, 68 (1965), 452-466.
15) M.A. Kaashoek and D.C. Lay, Ascent, descent, and commuting perturbations, Trans. Amer. Math. Soc., 189 (1972), 35-47.
16) S. Kaniel and M. Schechter, Spectral theory for Fredholm operators, Comm. Pure Appl. Math., 16 (1963), 423-448.
17) T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math., 6 (1958), 261-322.
18) T. Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 132, Springer-Verlag, New York, 1966.
19) J.P. Labrousse, Conditions nécessaires et sufisantes pour qu'un opérateur soit decomposable au sens de Kato, C.R. Acad. Sci. Paris Sér. A-B, 284 (1977), A295-A298.
20) J. Lambek, Lectures on rings and modules, Waltham, Massachusetts-Toronto-London, Blaisdell, 1966.
21) D.C. Lay, Spectral analysis using ascent, descent, nullity and defect, Math. Ann., 184 (1970), 197-214.
22) A.M. Sinclair, Automatic continuity of linear operators, London Math. Society Lecture Note Series, 21, Cambridge Univ. Press, Cambridge, 1976.
23) A.M. Sinclair and A.W. Tullo, Noetherian Banach algebras are finite dimensional, Math. Ann., 211 (1974), 151-153.
24) B. Yood, Properties of linear transformations preserved under addition of a completely continuous transformation, Duke Math. J., 18 (1951), 599-612.
Right : [1] H Bart and D. C. Lay, Poles of a generalized resolvent operator, Proc. Roy. Irish Acad. Sect. A, 1974, 147-168.
[2] S. R. Caradus, W. E. Pfaffenberger and B. Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Applied Mathematics, 9, Marcel Dekker, New York, 1974.
[3] P. A. Fillmore and J. P. Williams, On operator ranges, Advances in Math., 7 (1971), 254-281.
[4] K. H. Förster, Über die Invarianz einiger Räume, die zum Operator T-λA gehören, Arch. Math., 17 (1966), 56-64.
[5] T. W. Gamelin, Decomposition theorems for Fredholm operators, Pacific J. Math., 15 (1965), 97-106.
[6] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966.
[7] M. A. Gol'dman and S. N. Krackovskii, Invariance of certain spaces connected with the operator A-λI, Soviet Math. Dokl., 5 (1964), 102-104.
[8] M. A. Gol'dman and S. N. Krackovskii, Some perturbations of a closed linear operator, Soviet Math. Dokl., 5 (1964), 1243-1245.
[9] S. Grabiner, Ranges of products of operators, Canad. J. Math., 26 (1974), 1430-1441.
[10] S. Grabiner, Finitely generated, Noetherian, and Artinian Banach modules, Indiana Univ. Math. J., 26 (1977), 413-425.
[11] S. Grabiner, Ascent, descent, and compact perturbations, Proc. Amer. Math. Soc., 71 (1978), 79-80.
[12] S. Grabiner, Spectral consequences of the existence of intertwining operators, Comment. Math. Prace Mat., to appear.
[13] B. E. Johnson and A. M. Sinclair, Continuity of linear operators commuting with continuous linear operators II, Trans. Amer. Math. Soc., 146 (1969), 533-540.
[14] M. A. Kaashoek, Stability theorems for closed linear operators, Nederl. Akad. Wetensch. Proc. Ser. A, 68 (1965), 452-466.
[15] M. A. Kaashoek and D. C. Lay, Ascent, descent, and commuting perturbations, Trans. Amer. Math. Soc., 189 (1972), 35-47.
[16] S. Kaniel and M. Schechter, Spectral theory for Fredholm operators, Comm. Pure Appl. Math., 16 (1963), 423-448.
[17] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math., 6 (1958), 261-322.
[18] T. Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 132, Springer-Verlag, New York, 1966.
[19] J. P. Labrousse, Conditions nécessaires et suffisantes pour qu'un opérateur soit decomposable au sens de Kato, C. R. Acad. Sci. Paris Sér. A-B, 284 (1977), A295-A298.
[20] J. Lambek, Lectures on rings and modules, Waltham, Massachusetts-Toronto-London, Blaisdell, 1966.
[21] D. C. Lay, Spectral analysis using ascent, descent, nullity and defect, Math. Ann., 184 (1970), 197-214.
[22] A. M. Sinclair, Automatic continuity of linear operators, London Math. Society Lecture Note Series, 21, Cambridge Univ. Press, Cambridge, 1976.
[23] A. M. Sinclair and A. W. Tullo, Noetherian Banach algebras are finite dimensional, Math. Ann., 211 (1974), 151-153.
[24] B. Yood, Properties of linear transformations preserved under addition of a completely continuous transformation, Duke Math. J., 18 (1951), 599-612.
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